Percolation on Transitive Graphs

Author: Easo, Philip

Year: 2025

Degree: Dissertation (Ph.D.)

Advisor: Hutchcroft, Tom

Committee Members: Tamuz, Omer; Hutchcroft, Tom; Zhang, Lingfu; Conlon, David

Option: Mathematics

DOI: 10.7907/899s-pe86

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.

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