Phase diagram for once-reinforced random walks on trees with exponential weighting scheme
type: Item
instance of: scholarly article
title: Phase diagram for once-reinforced random walks on trees with exponential weighting scheme
zbMATH Open document ID: 1202.60068
author: M. Takei
author: Masaki Takeshima
published in: Statistics \& Probability Letters
publication date: 2008-11-25T00:00:00Z
review text: The reinforced random walk on a graph is defined by a weighting scheme that depends on the current local times of the walker and prefers steps to locations previously visited. The once-edge-reinforced random walk gives initial weight one to any edge and increases it by some fixed amount as soon as the edge has been crossed at least once; afterwards the weight remainsu unchanged. In this model, the absence of a recurrence-transience phase transition is known. The authors introduce a variant of a once-reinforced random walk on trees, which admits such a transition. For trees of bounded degree and supercritical Galton-Watson trees, they can give the whole picture of the phase diagram.
reviewed by: W. König
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 5372840
zbMATH Keywords: self-interacting random walks
zbMATH Keywords: reinforced random walk
zbMATH Keywords: recurrence and transience
zbMATH Keywords: phase diagram
MaRDI profile type: Publication
full work available at URL: j.spl.2008.05.006
OpenAlex ID: W2044165218
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DOI: 10.1016/J.SPL.2008.05.006
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description: scientific article; zbMATH DE number 5372840