Continuous-time vertex reinforced jump processes on Galton-Watson trees
type: Item
instance of: scholarly article
title: Continuous-time vertex reinforced jump processes on Galton-Watson trees
zbMATH Open document ID: 1260.60174
DOI: 10.1214/11-AAP811
author: Anne-Laure Basdevant
author: Arvind Singh
published in: The Annals of Applied Probability
publication date: 2012-09-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1005.3607
full work available at URL: https://projecteuclid.org/euclid.aoap/1344614210
review text: A random walk \(X(t)\) with continuous time \(t\) is defined on the vertices of an infinite supercritical Galton-Watson tree with mean offspring that is finite and larger than one. Conditional on \(X(s)\) for values of \(s\) up to \(t\) where \(X(t)=u\), the process jumps to a neighbor \(v\) of \(u\) with transition rate proportional to the current duration time at \(v\) plus a positive constant \(c\). The critical value of \(c\) for recurrence/transience is proved to be unique and is explicitly given. The phase transitions are specified and compared to those of a discrete-time random walk in a certain random environment.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 05C81
zbMATH DE Number: 6083950
zbMATH Keywords: reinforced processes
zbMATH Keywords: random walks on trees
zbMATH Keywords: branching processes
zbMATH Keywords: phase transition
MaRDI profile type: Publication
arXiv ID: 1005.3607
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description: scientific article; zbMATH DE number 6083950