[
    {
        "id": "thesis:17315",
        "collection": "thesis",
        "collection_id": "17315",
        "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05302025-191944015",
        "primary_object_url": {
            "basename": "Easo 2025 Percolation_on_transitive_graphs.pdf",
            "content": "final",
            "filesize": 2487741,
            "license": "other",
            "mime_type": "application/pdf",
            "url": "/17315/3/Easo 2025 Percolation_on_transitive_graphs.pdf",
            "version": "v5.0.0"
        },
        "type": "thesis",
        "title": "Percolation on Transitive Graphs",
        "author": [
            {
                "family_name": "Easo",
                "given_name": "Philip",
                "orcid": "0000-0002-5606-3727",
                "clpid": "Easo-Philip"
            }
        ],
        "thesis_advisor": [
            {
                "family_name": "Hutchcroft",
                "given_name": "Tom",
                "orcid": "0000-0003-0061-593X",
                "clpid": "Hutchcroft-Tom"
            }
        ],
        "thesis_committee": [
            {
                "family_name": "Tamuz",
                "given_name": "Omer",
                "orcid": "0000-0002-0111-0418",
                "clpid": "Tamuz-O"
            },
            {
                "family_name": "Hutchcroft",
                "given_name": "Tom",
                "orcid": "0000-0003-0061-593X",
                "clpid": "Hutchcroft-Tom"
            },
            {
                "family_name": "Zhang",
                "given_name": "Lingfu",
                "orcid": "0000-0002-4794-7678",
                "clpid": "Zhang-Lingfu"
            },
            {
                "family_name": "Conlon",
                "given_name": "David",
                "orcid": "0000-0001-5899-1829",
                "clpid": "Conlon-David"
            }
        ],
        "local_group": [
            {
                "literal": "div_pma"
            }
        ],
        "abstract": "Percolation on a transitive graph is an idealized mathematical model for a homogeneous system undergoing a phase transition. We will investigate how the geometry of an infinite transitive graph determines whether percolation undergoes a phase transition, and if so, at what critical point. Building on these ideas, we will develop a new theory of percolation on finite transitive graphs. This theory unifies the percolation phase transition on infinite transitive graphs with the giant-cluster phase transition in the celebrated Erd\u0151s-R\u00e9nyi model from combinatorics.",
        "doi": "10.7907/899s-pe86",
        "publication_date": "2025",
        "thesis_type": "phd",
        "thesis_year": "2025"
    }
]