On the Time Constant in a Dependent First Passage Percolation Model

TL;DR

This paper investigates a dependent first passage percolation model, demonstrating that its asymptotic shape varies continuously with the coloring law, using couplings with greedy lattice animals.

Contribution

It establishes the continuous dependence of the asymptotic shape on the coloring law in a dependent first passage percolation model.

Findings

Asymptotic shape depends continuously on the coloring law

Uses couplings with greedy lattice animals for proof

Extends understanding of dependent percolation models

Abstract

We pursue the study of a random coloring first passage percolation model introduced by Fontes and Newman. We prove that the asymptotic shape of this first passage percolation model continuously depends on the law of the coloring. The proof uses several couplings, particularly with greedy lattice animals.