First passage percolation and competition models

TL;DR

This survey explores first passage percolation as a model for fluid spread on graphs and examines its links to stochastic growth and competition models, highlighting key results and techniques.

Contribution

It provides a comprehensive overview of results and methods in first passage percolation and its connection to stochastic growth and competition models.

Findings

Summarizes key results in first passage percolation.

Details connections to stochastic growth models.

Highlights techniques used in the field.

Abstract

This paper is a survey of various results and techniques in first passage percolation, a random process modeling a spreading fluid on an infinite graph. The latter half of the paper focuses on the connection between first passage percolation and a certain class of stochastic growth and competition models.