A temporal perspective on the rate of convergence in first-passage percolation under a moment condition

TL;DR

This paper investigates the precise rate at which the probability of deviations decreases in the shape theorem of first-passage percolation, focusing on a temporal perspective under a moment condition.

Contribution

It provides a detailed asymptotic rate of decay for deviation probabilities in the temporal setting, complementing previous spatial analyses.

Findings

Derived the asymptotic decay rate for deviation probabilities

Established results under a specific moment condition

Extended understanding of convergence in first-passage percolation

Abstract

We study the rate of convergence in the Shape Theorem of first-passage percolation, obtaining the precise asymptotic rate of decay for the probability of linear order deviations under a moment condition. Our results are stated for a given time and complements recent work by the same author, in which the rate of convergence was studied from the standard spatial perspective.