Karoline Durbin : Phase transitions: an introduction through percolation

Posted by Josh Fletcher , part of the MATH Club.

At

Oct. 14, 2022, 2 p.m.

In

612 SEO

Abstract

Percolation is a probabilistic model for constructing random subgraphs of the n-dimensional grid by removing edges independently. Originally motivated by statistical physics, percolation has found purchase in many other areas of mathematics. Of particular interest is the fact that percolation undergoes a "phase transition" depending on the choice of the probability of removing an edge. In this talk, we will define precisely what this means, and outline a proof to show the existence of a critical threshold.