Quenched lower large deviation for the first passage time of the frog model in random initial configurations (Stochastic Analysis on Large Scale Interacting Systems)

Abstract

We consider the so-called frog model with random initial configurations. The dynamics of this model are described as follows: Some particles are randomly assigned to 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. In this paper, we study the behavior of the first passage time at which an active particle reaches a target site, and provide an upper bound on a quenched lower large deviation for the first passage time.