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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 08 Dec 2023 12:17:26 +0000Counterexamples for percolation on unimodular random graphs
https://resolver.caltech.edu/CaltechAUTHORS:20210922-193309642
Authors: Angel, Omer; Hutchcroft, Tom
Year: 2018
DOI: 10.1090/conm/719/14465
We construct an example of a bounded degree, nonamenable, unimodular random rooted graph with p_c = p_u for Bernoulli bond percolation, as well as an example of a bounded degree, unimodular random rooted graph with p_c < 1 but with an infinite cluster at criticality. These examples show that two well-known conjectures of Benjamini and Schramm are false when generalised from transitive graphs to unimodular random rooted graphs.https://authors.library.caltech.edu/records/5d27n-a1k66