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Frog models on trees through renewal theory

Part of: Special processes Time-dependent statistical mechanics (dynamic and nonequilibrium)

Published online by Cambridge University Press:  16 November 2018

Sandro Gallo  and
Pablo M. Rodriguez
Sandro Gallo*
Affiliation:
UFSCar
Pablo M. Rodriguez*
Affiliation:
USP
*
* Postal address: Departamento de Estatística, UFSCar, Rodovia Washington Luiz, km 235, CEP 13565-905, São Carlos, SP, Brasil. Email address: sandrodobrasil@gmail.com
** Postal address: Instituto de Ciências Matemáticas e de Computação, USP, Av. Trabalhador são-carlense 400 - Centro, CEP 13560-970, São Carlos, SP, Brasil.
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Abstract

We study a class of growing systems of random walks on regular trees, known as frog models with geometric lifetime in the literature. With the help of results from renewal theory, we derive new bounds for their critical parameters. Our approach also improves the existing bounds for the critical parameter of a percolation model on trees known as cone percolation.

Keywords

Frog modelcritical probabilitycone percolationhomogeneous treerenewal theory

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60K05: Renewal theory 82C41: Dynamics of random walks, random surfaces, lattice animals, etc.
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 3 , September 2018 , pp. 887 - 899
Copyright
Copyright © Applied Probability Trust 2018 

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