First passage percolation and competition models

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.

24 pages including references

References in corpus (3)

• Limiting shape for directed percolation models
• Toeplitz determinants, random growth and determinantal processes
• A GUE Central Limit Theorem and Universality of Directed First and Last Passage Site Percolation