Deviation bounds for the first passage time in the frog model

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.