1 April 2014 Localization for linearly edge reinforced random walks
Omer Angel, Nicholas Crawford, Gady Kozma
Duke Math. J. 163(5): 889-921 (1 April 2014). DOI: 10.1215/00127094-2644357


We prove that the linearly edge reinforced random walk (LRRW) on any graph with bounded degrees is recurrent for sufficiently small initial weights. In contrast, we show that for nonamenable graphs the LRRW is transient for sufficiently large initial weights, thereby establishing a phase transition for the LRRW on nonamenable graphs. While we rely on the equivalence of the LRRW to a mixture of Markov chains, the proof does not use the so-called magic formula which is central to most work on this model. We also derive analogous results for the vertex reinforced jump process.


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Omer Angel. Nicholas Crawford. Gady Kozma. "Localization for linearly edge reinforced random walks." Duke Math. J. 163 (5) 889 - 921, 1 April 2014. https://doi.org/10.1215/00127094-2644357


Published: 1 April 2014
First available in Project Euclid: 26 March 2014

zbMATH: 1302.60129
MathSciNet: MR3189433
Digital Object Identifier: 10.1215/00127094-2644357

Primary: 60K35
Secondary: 60K37

Rights: Copyright © 2014 Duke University Press

Vol.163 • No. 5 • 1 April 2014
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