Ekaterina Toropova: On the topic of first passage percolation

Abstract

First passage percolation was originally introduced to model the flow of a fluid through a random medium. In this framework, each edge of a square lattice is assigned a non-negative random variable, representing the time to traverse that edge. For any two points, \(x\) and \(y\), within this lattice, we define \(T(x,y)\) as the minimum time necessary to travel from \(x\) to \(y\); this defines a random metric on the lattice. The ultimate goal of first passage percolation is to understand this metric at the macroscopic level.

I will give an introduction to the model, an overview of results in this area, and a description of my current work in this field.