Percolation on Transitive Graphs

Citation

Easo, Philip (2025) Percolation on Transitive Graphs. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/899s-pe86. https://resolver.caltech.edu/CaltechTHESIS:05302025-191944015

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 Erdős-Rényi model from combinatorics.

Item Type:

Thesis (Dissertation (Ph.D.))

Subject Keywords:

Percolation

Degree Grantor:

California Institute of Technology

Division:

Physics, Mathematics and Astronomy

Major Option:

Mathematics

Awards:

Scott Russell Johnson Graduate Dissertation Prize in Mathematics, 2025. Scott Russell Johnson Prize for Excellence in Graduate Studies, 2023.

Thesis Availability:

Public (worldwide access)

Research Advisor(s):

Hutchcroft, Tom

Thesis Committee:

Tamuz, Omer (chair)
Hutchcroft, Tom
Zhang, Lingfu
Conlon, David

Defense Date:

28 May 2025

Non-Caltech Author Email:

philipeaso (AT) gmail.com

Record Number:

CaltechTHESIS:05302025-191944015

Persistent URL:

https://resolver.caltech.edu/CaltechTHESIS:05302025-191944015

DOI:

10.7907/899s-pe86

ORCID:

Author	ORCID
Easo, Philip	0000-0002-5606-3727

Default Usage Policy:

No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

17315

Collection:

CaltechTHESIS

Deposited By:

Philip Easo

Deposited On:

04 Jun 2025 18:29

Last Modified:

17 Jun 2025 18:37

Thesis Files

PDF - Final Version
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