Article records
https://feeds.library.caltech.edu/people/Tamuz-O/article.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 12 Apr 2024 14:24:15 +0000Correcting systematic effects in a large set of photometric light curves
https://resolver.caltech.edu/CaltechAUTHORS:20161109-161950022
Authors: {'items': [{'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'O.'}, 'orcid': '0000-0002-0111-0418'}, {'id': 'Mazeh-T', 'name': {'family': 'Mazeh', 'given': 'T.'}}, {'id': 'Zucker-S', 'name': {'family': 'Zucker', 'given': 'S.'}}]}
Year: 2005
DOI: 10.1111/j.1365-2966.2004.08585.x
We suggest a new algorithm to remove systematic effects in a large set of lightcurves obtained by a photometric survey. The algorithm can remove systematic effects, like the ones associated with atmospheric extinction, detector efficiency, or PSF changes over the detector. The algorithm works without any prior knowledge of the effects, as long as they linearly appear in many stars of the sample. The approach, which was originally developed to remove atmospheric extinction effects, is based on a lower rank approximation of matrices, an approach which was already suggested and used in chemometrics, for example. The proposed algorithm is specially useful in cases where the uncertainties of the measurements are unequal. For equal uncertainties the algorithm reduces to the Principal Components Analysis (PCA) algorithm. We present a simulation to demonstrate the effectiveness of the proposed algorithm and point out its potential, in search for transit candidates in particular.https://authors.library.caltech.edu/records/6t7fq-5s958Automated analysis of eclipsing binary light curves - II. Statistical analysis of OGLE LMC eclipsing binaries
https://resolver.caltech.edu/CaltechAUTHORS:20161109-163450950
Authors: {'items': [{'id': 'Mazeh-T', 'name': {'family': 'Mazeh', 'given': 'T.'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'O.'}, 'orcid': '0000-0002-0111-0418'}, {'id': 'North-P', 'name': {'family': 'North', 'given': 'P.'}}]}
Year: 2006
DOI: 10.1111/j.1365-2966.2006.10050.x
In the first paper of this series, we presented EBAS – Eclipsing Binary Automated Solver, a new fully automated algorithm to analyse the light curves of eclipsing binaries, based on the EBOP code. Here, we apply the new algorithm to the whole sample of 2580 binaries found in the Optical Gravitational Lensing Experiment (OGLE) Large Magellanic Cloud (LMC) photometric survey and derive the orbital elements for 1931 systems. To obtain the statistical properties of the short-period binaries of the LMC, we construct a well-defined subsample of 938 eclipsing binaries with main-sequence B-type primaries. Correcting for observational selection effects, we derive the distributions of the fractional radii of the two components and their sum, the brightness ratios and the periods of the short-period binaries. Somewhat surprisingly, the results are consistent with a flat distribution in log P between 2 and 10 d. We also estimate the total number of binaries in the LMC with the same characteristics, and not only the eclipsing binaries, to be about 5000. This figure leads us to suggest that (0.7 ± 0.4) per cent of the main-sequence B-type stars in the LMC are found in binaries with periods shorter than 10 d. This frequency is substantially smaller than the fraction of binaries found by small Galactic radial-velocity surveys of B stars. On the other hand, the binary frequency found by Hubble Space Telescope (HST) photometric searches within the late main-sequence stars of 47 Tuc is only slightly higher and still consistent with the frequency we deduced for the B stars in the LMC.https://authors.library.caltech.edu/records/s5ddn-sc375Automated analysis of eclipsing binary light curves - I. EBAS - a new Eclipsing Binary Automated Solver with EBOP
https://resolver.caltech.edu/CaltechAUTHORS:20161109-162833455
Authors: {'items': [{'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'O.'}, 'orcid': '0000-0002-0111-0418'}, {'id': 'Mazeh-T', 'name': {'family': 'Mazeh', 'given': 'T.'}}, {'id': 'North-P', 'name': {'family': 'North', 'given': 'P.'}}]}
Year: 2006
DOI: 10.1111/j.1365-2966.2006.10049.x
We present a new algorithm, Eclipsing Binary Automated Solver (EBAS), to analyse light curves of eclipsing binaries. The algorithm is designed to analyse large numbers of light curves, and is therefore based on the relatively fast EBOP code. To facilitate the search for the best solution, EBAS uses two parameter transformations. Instead of the radii of the two stellar components, EBAS uses the sum of radii and their ratio, while the inclination is transformed into the impact parameter. To replace human visual assessment, we introduce a new 'alarm' goodness-of-fit statistic that takes into account correlation between neighbouring residuals. We perform extensive tests and simulations that show that our algorithm converges well, finds a good set of parameters and provides reasonable error estimation.https://authors.library.caltech.edu/records/2fj5e-fqq81Photometric follow-up of the transiting planet WASP-1b
https://resolver.caltech.edu/CaltechAUTHORS:20161109-163957800
Authors: {'items': [{'id': 'Shporer-A', 'name': {'family': 'Shporer', 'given': 'A.'}, 'orcid': '0000-0002-1836-3120'}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'O.'}, 'orcid': '0000-0002-0111-0418'}, {'id': 'Zucker-S', 'name': {'family': 'Zucker', 'given': 'S.'}}, {'id': 'Mazeh-T', 'name': {'family': 'Mazeh', 'given': 'T.'}}]}
Year: 2007
DOI: 10.1111/j.1365-2966.2007.11537.x
We report on photometric follow-up of the recently discovered transiting planet WASP-1b. We observed two transits with the Wise Observatory 1-m telescope, and used a variant of the Eclipsing Binary Orbit Program (EBOP) code together with the Sys-Rem detrending approach to fit the light curve. Assuming a stellar mass of 1.15 M_⊙, we derived a planetary radius of R_p= 1.40 ± 0.06R_J and mass of M_p= 0.87 ± 0.07M_J. An uncertainty of 15 per cent in the stellar mass results in an additional systematic uncertainty of 5 per cent in the planetary radius and of 10 per cent in planetary mass. Our observations yielded a slightly better ephemeris for the centre of the transit: T_c [HJD]= (245 4013.3127 ± 0.0004) +N_(tr)(2.51996 ± 0.00002). The new planet is an inflated, low-density planet, similar to HAT-P-1b and HD 209458b.https://authors.library.caltech.edu/records/5x592-8wn14Iterative maximum likelihood on networks
https://resolver.caltech.edu/CaltechAUTHORS:20161109-165317769
Authors: {'items': [{'id': 'Mossel-E', 'name': {'family': 'Mossel', 'given': 'Elchanan'}, 'orcid': '0000-0001-7812-7886'}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2010
DOI: 10.1016/j.aam.2009.11.004
We consider n agents located on the vertices of a connected graph. Each agent v receives a signal X_v(0)∼N(μ,1) where μ is an unknown quantity. A natural iterative way of estimating μ is to perform the following procedure. At iteration t+1 let X_v(t+1) be the average of X_v(t) and of X_w(t) among all the neighbors w of v. It is well known that this procedure converges to X(∞) = 1/2 |E|^(−1) Σ d_v X_v where dv is the degree of v.
In this paper we consider a variant of simple iterative averaging, which models "greedy" behavior of the agents. At iteration t, each agent v declares the value of its estimator X_v(t) to all of its neighbors. Then, it updates X_v(t+1) by taking the maximum likelihood (or minimum variance) estimator of μ, given X_v(t) and X_w(t) for all neighbors w of v, and the structure of the graph.
We give an explicit efficient procedure for calculating X_v(t), study the convergence of the process as t→∞ and show that if the limit exists then X_v(∞)=X_w(∞) for all v and w. For graphs that are symmetric under actions of transitive groups, we show that the process is efficient. Finally, we show that the greedy process is in some cases more efficient than simple averaging, while in other cases the converse is true, so that, in this model, "greed" of the individual agents may or may not have an adverse affect on the outcome.
The model discussed here may be viewed as the maximum likelihood version of models studied in Bayesian Economics. The ML variant is more accessible and allows in particular to show the significance of symmetry in the efficiency of estimators using networks of agents.https://authors.library.caltech.edu/records/mr5rg-bsq25Complete Characterization of Functions Satisfying the Conditions of Arrow's Theorem
https://resolver.caltech.edu/CaltechAUTHORS:20161110-073042338
Authors: {'items': [{'id': 'Mossel-E', 'name': {'family': 'Mossel', 'given': 'Elchanan'}, 'orcid': '0000-0001-7812-7886'}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2012
DOI: 10.1007/s00355-011-0547-0
Arrow's theorem implies that a social welfare function satisfying Transitivity, the Weak Pareto Principle (Unanimity), and Independence of Irrelevant Alternatives (IIA) must be dictatorial. When non-strict preferences are also allowed, a dictatorial social welfare function is defined as a function for which there exists a single voter whose strict preferences are followed. This definition allows for many different dictatorial functions, since non-strict preferences of the dictator are not necessarily followed. In particular, we construct examples of dictatorial functions which do not satisfy Transitivity and IIA. Thus Arrow's theorem, in the case of non-strict preferences, does not provide a complete characterization of all social welfare functions satisfying Transitivity, the Weak Pareto Principle, and IIA. The main results of this article provide such a characterization for Arrow's theorem, as well as for follow up results by Wilson. In particular, we strengthen Arrow's and Wilson's result by giving an exact if and only if condition for a function to satisfy Transitivity and IIA (and the Weak Pareto Principle). Additionally, we derive formulae for the number of functions satisfying these conditions.https://authors.library.caltech.edu/records/148nq-15p36A lower bound on seller revenue in single buyer monopoly auctions
https://resolver.caltech.edu/CaltechAUTHORS:20161114-065718415
Authors: {'items': [{'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2013
DOI: 10.1016/j.orl.2013.05.011
We consider a monopoly seller who optimally auctions a single object to a single potential buyer, with a known distribution of valuations. We show that a tight lower bound on the seller's expected revenue is 1/e times the geometric expectation of the buyer's valuation, and that this bound is uniquely achieved for the equal revenue distribution. We show also that when the valuation's expectation and geometric expectation are close, then the seller's expected revenue is close to the expected valuation.https://authors.library.caltech.edu/records/ee3ak-awj41Testing Booleanity and the Uncertainty Principle
https://resolver.caltech.edu/CaltechAUTHORS:20161110-144803099
Authors: {'items': [{'id': 'Gur-Tom', 'name': {'family': 'Gur', 'given': 'Tom'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2013
DOI: 10.4086/cjtcs.2013.014
Let f : {-1,1}^n → R be a real function on the hypercube, given by its discrete
Fourier expansion, or, equivalently, represented as a multilinear polynomial. We say that it is
Boolean if its image is in {-1;1}.
We show that every function on the hypercube with a sparse Fourier expansion must
either be Boolean or far from Boolean. In particular, we show that a multilinear polynomial
with at most k terms must either be Boolean, or output values different than -1 or 1 for a
fraction of at least 2=(k+2)² of its domain.
It follows that given oracle access to f, together with the guarantee that its representation
as a multilinear polynomial has at most k terms, one can test Booleanity using O(k²) queries.
We show an Ω(k) queries lower bound for this problem.
Our proof crucially uses Hirschman's entropic version of Heisenberg's uncertainty principle.https://authors.library.caltech.edu/records/ex9gs-37q03Making Consensus Tractable
https://resolver.caltech.edu/CaltechAUTHORS:20161110-081650257
Authors: {'items': [{'id': 'Mossel-E', 'name': {'family': 'Mossel', 'given': 'Elchanan'}, 'orcid': '0000-0001-7812-7886'}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2013
DOI: 10.1145/2542174.2542176
We study a model of consensus decision making in which a finite group of Bayesian agents has to choose between one of two courses of action. Each member of the group has a private and independent signal at his or her disposal, giving some indication as to which action is optimal. To come to a common decision, the participants perform repeated rounds of voting. In each round, each agent casts a vote in favor of one of the two courses of action, reflecting his or her current belief, and observes the votes of the rest.
We provide an efficient algorithm for the calculation the agents have to perform and show that consensus is always reached and that the probability of reaching a wrong decision decays exponentially with the number of agents.https://authors.library.caltech.edu/records/5shpz-p9366Asymptotic learning on Bayesian social networks
https://resolver.caltech.edu/CaltechAUTHORS:20161114-072802716
Authors: {'items': [{'id': 'Mossel-E', 'name': {'family': 'Mossel', 'given': 'Elchanan'}, 'orcid': '0000-0001-7812-7886'}, {'id': 'Sly-A', 'name': {'family': 'Sly', 'given': 'Allan'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2014
DOI: 10.1007/s00440-013-0479-y
We study a standard model of economic agents on the nodes of a social network graph who learn a binary "state of the world" S, from initial signals, by repeatedly observing each other's best guesses. Asymptotic learning is said to occur on a family of graphs G_n=(V_n,E_n) with |V_n|→∞ if with probability tending to 1 as n→∞ all agents in G_n eventually estimate S correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.https://authors.library.caltech.edu/records/mftzy-6bb79Majority Dynamics and Aggregation of Information in Social Networks
https://resolver.caltech.edu/CaltechAUTHORS:20161114-070336278
Authors: {'items': [{'id': 'Mossel-E', 'name': {'family': 'Mossel', 'given': 'Elchanan'}, 'orcid': '0000-0001-7812-7886'}, {'id': 'Neeman-J', 'name': {'family': 'Neeman', 'given': 'Joe'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2014
DOI: 10.1007/s10458-013-9230-4
Consider n individuals who, by popular vote, choose among q ≥ 2 alternatives, one of which is "better" than the others. Assume that each individual votes independently at random, and that the probability of voting for the better alternative is larger than the probability of voting for any other. It follows from the law of large numbers that a plurality vote among the n individuals would result in the correct outcome, with probability approaching one exponentially quickly as n → ∞.
Our interest in this paper is in a variant of the process above where, after forming their initial opinions, the voters update their decisions based on some interaction with their neighbors in a social network. Our main example is "majority dynamics", in which each voter adopts the most
popular opinion among its friends. The interaction repeats for some number of rounds and is then followed by a population-wide plurality vote. The question we tackle is that of "efficient aggregation of information": in which cases is the better alternative chosen with probability approaching one as n → ∞? Conversely, for which sequences of growing graphs does aggregation fail, so that the wrong alternative gets chosen with probability bounded away from zero? We construct a family of examples in which interaction prevents efficient aggregation of information, and give a condition on the social network which ensures that aggregation occurs. For the case of majority dynamics we also investigate the question of unanimity in the
limit. In particular, if the voters' social network is an expander graph, we show that if the initial population is sufficiently biased towards a particular alternative then that alternative will eventually become the unanimous preference of the entire population.https://authors.library.caltech.edu/records/1xdge-aph37Scenery Reconstruction on Finite Abelian Groups
https://resolver.caltech.edu/CaltechAUTHORS:20161110-120309955
Authors: {'items': [{'id': 'Finucane-H', 'name': {'family': 'Finucane', 'given': 'Hilary'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}, {'id': 'Yaari-Y', 'name': {'family': 'Yaari', 'given': 'Yariv'}}]}
Year: 2014
DOI: 10.1016/j.spa.2014.03.012
We consider the question of when a random walk on a finite abelian group with a given step distribution can be used to reconstruct a binary labeling of the elements of the group, up to a shift. Matzinger and Lember (2006) give a sufficient condition for reconstructability on cycles. While, as we show, this condition is not in general necessary, our main result is that it is necessary when the length of the cycle is prime and larger than 5, and the step distribution has only rational probabilities. We extend this result to other abelian groups.https://authors.library.caltech.edu/records/g3mvt-q2747Majority Dynamics and the Retention of Information
https://resolver.caltech.edu/CaltechAUTHORS:20161114-074309531
Authors: {'items': [{'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}, {'id': 'Tessler-R-J', 'name': {'family': 'Tessler', 'given': 'Ran J.'}}]}
Year: 2015
DOI: 10.1007/s11856-014-1148-2
We consider a group of agents connected by a social network who participate in majority dynamics: each agent starts with an opinion in {−1, +1} and repeatedly updates it to match the opinion of the majority of its neighbors.
We assume that one of {−1, +1} is the "correct" opinion S, and consider a setting in which the initial opinions are independent conditioned on S, and biased towards it. They hence contain enough information to reconstruct S with high probability. We ask whether it is still possible to reconstruct S from the agents' opinions after many rounds of updates.
While this is not the case in general, we show that indeed, for a large family of bounded degree graphs, information on S is retained by the process of majority dynamics.
Our proof technique yields novel combinatorial results on majority dynamics on both finite and infinite graphs, with applications to zero temperature Ising models.https://authors.library.caltech.edu/records/sehfj-w7m20Furstenberg entropy realizations for virtually free groups and lamplighter groups
https://resolver.caltech.edu/CaltechAUTHORS:20161114-085457028
Authors: {'items': [{'id': 'Hartman-Y', 'name': {'family': 'Hartman', 'given': 'Yair'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2015
DOI: 10.1007/s11854-015-0016-2
Let (G,µ) be a discrete group with a generating probability measure. Nevo showed that if G has Kazhdan's property (T), then there exists ɛ > 0 such that the Furstenberg entropy of any (G,µ)-stationary ergodic space is either 0 or larger than ɛ. Virtually free groups, such as SL_2(ℤ), do not have property (T), and neither do their extensions, such as surface groups. For virtually free groups, we construct stationary actions with arbitrarily small, positive entropy. The construction involves building and lifting spaces of lamplighter groups. For some classical lamplighter gropus, these spaces realize a dense set of entropies between 0 and the Poisson boundary entropy.https://authors.library.caltech.edu/records/yr4pm-hz383Strategic Learning and the Topology of Social Networks
https://resolver.caltech.edu/CaltechAUTHORS:20151029-144956303
Authors: {'items': [{'id': 'Mossel-E', 'name': {'family': 'Mossel', 'given': 'Elchanan'}, 'orcid': '0000-0001-7812-7886'}, {'id': 'Sly-A', 'name': {'family': 'Sly', 'given': 'Allan'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2015
DOI: 10.3982/ECTA12058
We consider a group of strategic agents who must each repeatedly take one of two possible actions. They learn which of the two actions is preferable from initial private signals and by observing the actions of their neighbors in a social network.https://authors.library.caltech.edu/records/ze2wh-d0577Property (T) and the Furstenberg Entropy of Nonsingular Actions
https://resolver.caltech.edu/CaltechAUTHORS:20161111-141359999
Authors: {'items': [{'id': 'Bowen-L', 'name': {'family': 'Bowen', 'given': 'Lewis'}}, {'id': 'Hartman-Y', 'name': {'family': 'Hartman', 'given': 'Yair'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2016
DOI: 10.1090/proc/12685
We establish a new characterization of property (T) in terms of the Furstenberg entropy of nonsingular actions. Given any generating measure μ on a countable group G, A. Nevo showed that a necessary condition for G to have property (T) is that the Furstenberg μ-entropy values of the ergodic, properly nonsingular G-actions are bounded away from zero. We show that this is also a sufficient condition.https://authors.library.caltech.edu/records/d3khd-chq05Transitive graphs uniquely determined by their local structure
https://resolver.caltech.edu/CaltechAUTHORS:20161111-141028249
Authors: {'items': [{'id': 'Frisch-J', 'name': {'family': 'Frisch', 'given': 'Joshua'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2016
DOI: 10.1090/proc/12901
We give an example of an infinite, vertex transitive graph that has the following property: it is the unique completion to a transitive graph of a large enough finite subgraph of itself.https://authors.library.caltech.edu/records/3xbk1-zwt83Graphical potential games
https://resolver.caltech.edu/CaltechAUTHORS:20160603-083016959
Authors: {'items': [{'id': 'Babichenko-Y', 'name': {'family': 'Babichenko', 'given': 'Yakov'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2016
DOI: 10.1016/j.jet.2016.03.010
We study the class of potential games that are also graphical games with respect to a given graph G of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of Markov random fields on G. From this characterization, and from the Hammersley–Clifford theorem, it follows that the potentials of such games can be decomposed into local potentials.https://authors.library.caltech.edu/records/4ps3z-8tg56Stabilizer rigidity in irreducible group actions
https://resolver.caltech.edu/CaltechAUTHORS:20161109-132848541
Authors: {'items': [{'id': 'Hartman-Y', 'name': {'family': 'Hartman', 'given': 'Yair'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2016
DOI: 10.1007/s11856-016-1424-4
We consider irreducible actions of locally compact product groups, and of higher rank semi-simple Lie groups. Using the intermediate factor theorems of Bader–Shalom and Nevo–Zimmer, we show that the action stabilizers, and all irreducible invariant random subgroups, are co-amenable in their normal closure. As a consequence, we derive rigidity results on irreducible actions that generalize and strengthen the results of Bader–Shalom and Stuck–Zimmer.https://authors.library.caltech.edu/records/qpymd-ajt43Unimodularity of Invariant Random Subgroups
https://resolver.caltech.edu/CaltechAUTHORS:20161111-145903029
Authors: {'items': [{'id': 'Biringer-I', 'name': {'family': 'Biringer', 'given': 'Ian'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2016
DOI: 10.1090/tran/6755
An invariant random subgroup H≤G is a random closed subgroup whose law is invariant to conjugation by all elements of G. When G is locally compact and second countable, we show that for every invariant random subgroup H≤G there almost surely exists an invariant measure on G/H. Equivalently, the modular function of H is almost surely equal to the modular function of G, restricted to H.
We use this result to construct invariant measures on orbit equivalence relations of measure preserving actions. Additionally, we prove a mass transport principle for discrete or compact invariant random subgroups.https://authors.library.caltech.edu/records/2bwkj-kyf78Opinion Exchange Dynamics
https://resolver.caltech.edu/CaltechAUTHORS:20161111-150254761
Authors: {'items': [{'id': 'Mossel-E', 'name': {'family': 'Mossel', 'given': 'Elchanan'}, 'orcid': '0000-0001-7812-7886'}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2017
DOI: 10.1214/14-PS230
The exchange of opinions between individuals is a fundamental social interaction that plays a role in nearly any social, political and economic process. While it is unlikely that a simple mathematical model can accurately describe the exchange of opinions between two people, one could hope to gain some insights on emergent phenomena that affect large groups of people.https://authors.library.caltech.edu/records/tw0pb-nsv65Generic Stationary Measures and Actions
https://resolver.caltech.edu/CaltechAUTHORS:20161114-092928470
Authors: {'items': [{'id': 'Bowen-L', 'name': {'family': 'Bowen', 'given': 'Lewis'}}, {'id': 'Hartman-Y', 'name': {'family': 'Hartman', 'given': 'Yair'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2017
DOI: 10.1090/tran/6803
Let G be a countably infinite group, and let μ be a generating probability measure on G. We study the space of μ-stationary Borel probability measures on a topological G space, and in particular on Z^G, where Z is any perfect Polish space. We also study the space of μ-stationary, measurable G-actions on a standard, nonatomic probability space.
Equip the space of stationary measures with the weak* topology. When μ has finite entropy, we show that a generic measure is an essentially free extension of the Poisson boundary of (G, μ). When Z is compact, this implies that the simplex of μ-stationary
measures on Z^G is a Poulsen simplex. We show that this is also the case for the simplex of stationary measures on {0, 1}^G.
We furthermore show that if the action of G on its Poisson boundary is essentially free then a generic measure is isomorphic to the Poisson boundary.
Next, we consider the space of stationary actions, equipped with a standard topology known as the weak topology. Here we show that when G has property (T), the
ergodic actions are meager. We also construct a group G without property (T) such that the ergodic actions are not dense, for some μ.
Finally, for a weaker topology on the set of actions, which we call the very weak topology, we show that a dynamical property (e.g., ergodicity) is topologically generic if and only if it is generic in the space of measures. There we also show a Glasner-King type 0-1 law stating that every dynamical property is either meager or residual.https://authors.library.caltech.edu/records/2wjwa-cq465The speed of sequential asymptotic learning
https://resolver.caltech.edu/CaltechAUTHORS:20170712-081145954
Authors: {'items': [{'id': 'Hann-Caruthers-W', 'name': {'family': 'Hann-Caruthers', 'given': 'Wade'}}, {'id': 'Martynov-V-V', 'name': {'family': 'Martynov', 'given': 'Vadim V.'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2018
DOI: 10.1016/j.jet.2017.11.009
In the classical herding literature, agents receive a private signal regarding a binary state of nature, and sequentially choose an action, after observing the actions of their predecessors. When the informativeness of private signals is unbounded, it is known that agents converge to the correct action and correct belief. We study how quickly convergence occurs, and show that it happens more slowly than it does when agents observe signals. However, we also show that the speed of learning from actions can be arbitrarily close to the speed of learning from signals. In particular, the expected time until the agents stop taking the wrong action can be either finite or infinite, depending on the private signal distribution. In the canonical case of Gaussian private signals we calculate the speed of convergence precisely, and show explicitly that, in this case, learning from actions is significantly slower than learning from signals.https://authors.library.caltech.edu/records/tgbga-5zw88Thompson's group F is not strongly amenable
https://resolver.caltech.edu/CaltechAUTHORS:20161111-131006027
Authors: {'items': [{'id': 'Hartman-Y', 'name': {'family': 'Hartman', 'given': 'Yair'}}, {'id': 'Juschenko-K', 'name': {'family': 'Juschenko', 'given': 'Kate'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}, {'id': 'Vahidi-Ferdowsi-P', 'name': {'family': 'Vahidi Ferdowsi', 'given': 'Pooya'}}]}
Year: 2019
DOI: 10.1017/etds.2017.49
We show that Thompson's group has a topological action on a compact metric space that is proximal and has no fixed points.https://authors.library.caltech.edu/records/5edh3-kv125Normal amenable subgroups of the automorphism group of the full shift
https://resolver.caltech.edu/CaltechAUTHORS:20161111-133444186
Authors: {'items': [{'id': 'Frisch-J', 'name': {'family': 'Frisch', 'given': 'Joshua'}}, {'id': 'Schlank-T', 'name': {'family': 'Schlank', 'given': 'Tomer'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2019
DOI: 10.1017/etds.2017.72
We show that every normal amenable subgroup of the automorphism group of the full shift is contained in its center. This follows from the analysis of this group's Furstenberg topological boundary, through the construction of a minimal and strongly proximal action. We extend this result to higher dimensional full shifts. This also provides a new proof of Ryan's theorem and of the fact that these groups contain free groups.https://authors.library.caltech.edu/records/dkhn3-n3274Choquet-Deny groups and the infinite conjugacy class property
https://resolver.caltech.edu/CaltechAUTHORS:20190725-090144871
Authors: {'items': [{'id': 'Frisch-J', 'name': {'family': 'Frisch', 'given': 'Joshua'}}, {'id': 'Hartman-Y', 'name': {'family': 'Hartman', 'given': 'Yair'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}, {'id': 'Vahidi-Ferdowsi-P', 'name': {'family': 'Vahidi Ferdowsi', 'given': 'Pooya'}}]}
Year: 2019
DOI: 10.4007/annals.2019.190.1.5
A countable discrete group G is called Choquet-Deny if for every non-degenerate probability measure μ on G, it holds that all bounded μ-harmonic functions are constant. We show that a finitely generated group G is Choquet-Deny if and only if it is virtually nilpotent. For general countable discrete groups, we show that G is Choquet-Deny if and only if none of its quotients has the infinite conjugacy class property. Moreover, when G is not Choquet-Deny, then this is witnessed by a symmetric, finite entropy, non-degenerate measure.https://authors.library.caltech.edu/records/t636j-2fq90Strong amenability and the infinite conjugacy class property
https://resolver.caltech.edu/CaltechAUTHORS:20191114-102021413
Authors: {'items': [{'id': 'Frisch-J', 'name': {'family': 'Frisch', 'given': 'Joshua'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}, {'id': 'Vahidi-Ferdowsi-P', 'name': {'family': 'Vahidi Ferdowsi', 'given': 'Pooya'}}]}
Year: 2019
DOI: 10.1007/s00222-019-00896-z
A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quotients have the infinite conjugacy class property.https://authors.library.caltech.edu/records/1f0pv-rf491Invariant random subgroups of semidirect products
https://resolver.caltech.edu/CaltechAUTHORS:20170712-084843331
Authors: {'items': [{'id': 'Biringer-I', 'name': {'family': 'Biringer', 'given': 'Ian'}}, {'id': 'Bowen-L', 'name': {'family': 'Bowen', 'given': 'Lewis'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2020
DOI: 10.1017/etds.2018.46
We study invariant random subgroups (IRSs) of semidirect products G=A⋊Γ. In particular, we characterize all IRSs of parabolic subgroups of SL_d(R), and show that all ergodic IRSs of R^d⋊SL_d(R) are either of the form R^d⋊K for some IRS of SL_d(R), or are induced from IRSs of Λ⋊SL(Λ), where Λhttps://authors.library.caltech.edu/records/nm5e3-25081Stochastic Dominance Under Independent Noise
https://resolver.caltech.edu/CaltechAUTHORS:20190405-101226198
Authors: {'items': [{'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}, {'id': 'Strack-P', 'name': {'family': 'Strack', 'given': 'Philipp'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2020
DOI: 10.1086/705555
Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g., uninsurable labor risk, house price risk) can affect the ordering of gambles. We show that, perhaps surprisingly, background risk can be strong enough to render lotteries that are ranked by their expectation ranked in terms of first-order stochastic dominance. We extend our results to second-order stochastic dominance and show how they lead to a novel and elementary axiomatization of mean-variance preferences.https://authors.library.caltech.edu/records/m9xak-tca52Social Learning Equilibria
https://resolver.caltech.edu/CaltechAUTHORS:20200521-152747894
Authors: {'items': [{'id': 'Mossel-E', 'name': {'family': 'Mossel', 'given': 'Elchanan'}, 'orcid': '0000-0001-7812-7886'}, {'id': 'Mueller-Frank-M', 'name': {'family': 'Mueller-Frank', 'given': 'Manuel'}}, {'id': 'Sly-A', 'name': {'family': 'Sly', 'given': 'Allan'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2020
DOI: 10.3982/ecta16465
We consider a large class of social learning models in which a group of agents face uncertainty regarding a state of the world, share the same utility function, observe private signals, and interact in a general dynamic setting. We introduce social learning equilibria, a static equilibrium concept that abstracts away from the details of the given extensive form, but nevertheless captures the corresponding asymptotic equilibrium behavior. We establish general conditions for agreement, herding, and information aggregation in equilibrium, highlighting a connection between agreement and information aggregation.https://authors.library.caltech.edu/records/yz2f6-maw09Unfriendly colorings of graphs with finite average degree
https://resolver.caltech.edu/CaltechAUTHORS:20200124-090354536
Authors: {'items': [{'id': 'Conley-C-T', 'name': {'family': 'Conley', 'given': 'Clinton T.'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2020
DOI: 10.1112/plms.12345
In an unfriendly coloring of a graph the color of every node mismatches that of the majority of its neighbors. We show that every probability measure preserving Borel graph with finite average degree admits a Borel unfriendly coloring almost everywhere. We also show that every bounded degree Borel graph of subexponential growth admits a Borel unfriendly coloring.https://authors.library.caltech.edu/records/ya229-k3e62Repeated Coordination with Private Learning
https://resolver.caltech.edu/CaltechAUTHORS:20190628-075628753
Authors: {'items': [{'id': 'Basu-Pathikrit', 'name': {'family': 'Basu', 'given': 'Pathikrit'}}, {'id': 'Chatterjee-Kalyan', 'name': {'family': 'Chatterjee', 'given': 'Kalyan'}}, {'id': 'Hoshino-Tetsuya', 'name': {'family': 'Hoshino', 'given': 'Tetsuya'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2020
DOI: 10.1016/j.jet.2020.105106
We study a repeated game with payoff externalities and observable actions where two players receive information over time about an underlying payoff-relevant state, and strategically coordinate their actions. Players learn about the true state from private signals, as well as the actions of others. They commonly learn the true state (Cripps et al., 2008), but do not coordinate in every equilibrium. We show that there exist stable equilibria in which players can overcome unfavorable signal realizations and eventually coordinate on the correct action, for any discount factor. For high discount factors, we show that in addition players can also achieve efficient payoffs.https://authors.library.caltech.edu/records/6590x-xqw57From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again
https://resolver.caltech.edu/CaltechAUTHORS:20200124-080643011
Authors: {'items': [{'id': 'Mu-Xiaosheng', 'name': {'family': 'Mu', 'given': 'Xiaosheng'}, 'orcid': '0000-0002-2868-5182'}, {'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}, {'id': 'Strack-Philipp', 'name': {'family': 'Strack', 'given': 'Philipp'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2021
DOI: 10.3982/ECTA17548
We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to Blackwell (1951), we show that generically an experiment is more informative than another in large samples if and only if it has higher Rényi divergences.https://authors.library.caltech.edu/records/x70d0-23195Rational Groupthink
https://resolver.caltech.edu/CaltechAUTHORS:20161111-135545798
Authors: {'items': [{'id': 'Harel-Matan', 'name': {'family': 'Harel', 'given': 'Matan'}}, {'id': 'Mossel-Elchanan', 'name': {'family': 'Mossel', 'given': 'Elchanan'}, 'orcid': '0000-0001-7812-7886'}, {'id': 'Strack-Philipp', 'name': {'family': 'Strack', 'given': 'Philipp'}, 'orcid': '0000-0002-7960-9243'}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2021
DOI: 10.1093/qje/qjaa026
We study how long-lived rational agents learn from repeatedly observing a private signal and each others' actions. With normal signals, a group of any size learns more slowly than just four agents who directly observe each others' private signals in each period. Similar results apply to general signal structures. We identify rational groupthink—in which agents ignore their private signals and choose the same action for long periods of time—as the cause of this failure of information aggregation.https://authors.library.caltech.edu/records/c9dkm-rs921Equitable Voting Rules
https://resolver.caltech.edu/CaltechAUTHORS:20210414-131421263
Authors: {'items': [{'id': 'Bartholdi-Laurent', 'name': {'family': 'Bartholdi', 'given': 'Laurent'}}, {'id': 'Hann-Caruthers-Wade', 'name': {'family': 'Hann-Caruthers', 'given': 'Wade'}}, {'id': 'Josyula-Maya', 'name': {'family': 'Josyula', 'given': 'Maya'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}, {'id': 'Yariv-L', 'name': {'family': 'Yariv', 'given': 'Leeat'}}]}
Year: 2021
DOI: 10.3982/ecta17032
May's theorem (1952), a celebrated result in social choice, provides the foundation for majority rule. May's crucial assumption of symmetry, often thought of as a procedural equity requirement, is violated by many choice procedures that grant voters identical roles. We show that a weakening of May's symmetry assumption allows for a far richer set of rules that still treat voters equally. We show that such rules can have minimal winning coalitions comprising a vanishing fraction of the population, but not less than the square root of the population size. Methodologically, we introduce techniques from group theory and illustrate their usefulness for the analysis of social choice questions.https://authors.library.caltech.edu/records/54q7t-dfp96Feasible Joint Posterior Beliefs
https://resolver.caltech.edu/CaltechAUTHORS:20210727-175655408
Authors: {'items': [{'id': 'Arieli-Itai', 'name': {'family': 'Arieli', 'given': 'Itai'}, 'orcid': '0000-0001-8663-5776'}, {'id': 'Babichenko-Yakov', 'name': {'family': 'Babichenko', 'given': 'Yakov'}, 'orcid': '0000-0002-6970-1601'}, {'id': 'Sandomirskiy-Fedor', 'name': {'family': 'Sandomirskiy', 'given': 'Fedor'}, 'orcid': '0000-0001-9886-3688'}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2021
DOI: 10.1086/714993
We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state and who observe some information structure. For two agents, we introduce a quantitative version of Aumann's agreement theorem and show that it is equivalent to a characterization of feasible distributions from a 1995 work by Dawid and colleagues. For any number of agents, we characterize feasible distributions in terms of a "no-trade" condition. We use these characterizations to study information structures with independent posteriors. We also study persuasion problems with multiple receivers, exploring the extreme feasible distributions.https://authors.library.caltech.edu/records/xww49-kn658Additive conjugacy and the Bohr compactification of orthogonal representations
https://resolver.caltech.edu/CaltechAUTHORS:20200124-084913765
Authors: {'items': [{'id': 'Chase-Zachary', 'name': {'family': 'Chase', 'given': 'Zachary'}, 'orcid': '0000-0001-7015-3537'}, {'id': 'Hann-Caruthers-Wade', 'name': {'family': 'Hann-Caruthers', 'given': 'Wade'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2021
DOI: 10.1007/s00208-021-02191-w
We say that two unitary or orthogonal representations of a finitely generated group G are additive conjugates if they are intertwined by an additive map, which need not be continuous. We associate to each representation of G a topological action that is a complete additive conjugacy invariant: the action of G by group automorphisms on the Bohr compactification of the underlying Hilbert space. Using this construction we show that the property of having almost invariant vectors is an additive conjugacy invariant. As an application we show that G is amenable if and only if there is a nonzero homomorphism from L²(G) into R/Z that is invariant to the G-action.https://authors.library.caltech.edu/records/gzavk-dpt69