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

Cited by in corpus (12)

• Sublinear variance in first-passage percolation for general distributions
• Percolation since Saint-Flour
• Subdiffusive concentration in first-passage percolation
• A simplified proof of the relation between scaling exponents in first-passage percolation
• Geodesics of Random Riemannian Metrics
• Interacting growth processes and invariant percolation
• Asymptotics for $2D$ Critical First Passage Percolation
• Busemann functions and infinite geodesics in two-dimensional first-passage percolation
• Geodesics of Random Riemannian Metrics: Supplementary Material
• Dissertation: Geodesics of Random Riemannian Metrics
• Differentiability at the edge of the percolation cone and related results in first-passage percolation
• Random Shortest Paths: Non-Euclidean Instances for Metric Optimization Problems