Localization for Linearly Edge Reinforced Random Walks

Details Localization for Linearly Edge Reinforced Random Walks Localization for Linearly Edge Reinforced Random Walks

2012-03-19

arxiv.org/abs/1203.4010v1

Mathematics

Probability

30 pages

Scientific paper

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 non-amenable graphs the LRRW is transient for sufficiently large initial weights, thereby establishing a phase transition for the LRRW on non-amenable graphs. While we rely on the description of the LRRW as a mixture of Markov chains, the proof does not use the magic formula. We also derive analogous results for the vertex reinforced jump process.

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