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Deviation bounds for the first passage time in the frog model

Part of: Equilibrium statistical mechanics Special processes

Published online by Cambridge University Press:  22 July 2019

Naoki Kubota
Naoki Kubota*
Affiliation:
College of Science and Technology, Nihon University
*
*Postal address: College of Science and Technology, Nihon University, 24-1, Narashinodai 7-chome, Funabashi-shi, Chiba 274-8501, Japan. Email address: kubota.naoki08@nihon-u.ac.jp
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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. 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.

Keywords

Frog modelegg modelsimple random walkrandom environmentlarge deviation inequalityconcentration inequality

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 82B43: Percolation
Type
Original Article
Information
Advances in Applied Probability , Volume 51 , Issue 1 , March 2019 , pp. 184 - 208
Copyright
© Applied Probability Trust 2019 

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