Deviation bounds for the first passage time in the frog model

TL;DR

This paper derives deviation bounds for the time it takes in the frog model for an active particle to reach a target, considering random initial configurations and the activation process.

Contribution

It provides new large deviation and concentration bounds for the first passage time in the frog model with random initial particle placements.

Findings

Established deviation bounds for first passage times

Derived concentration inequalities for activation times

Analyzed the impact of initial configurations on passage times

Abstract

We consider the so-called frog model with random initial configurations. The dynamics of this model is described as follows: Some particles are randomly assigned on any site of the multidimensional cubic lattice. Initially, only particles at the origin are active and these independently perform simple random walks. The other particles are sleeping and do not move at first. When sleeping particles are hit by an active particle, they become active and start moving in a similar fashion. The aim of this paper is to derive large deviation and concentration bounds for the first passage time at which an active particle reaches a target site.