Random walk in changing environment

Gideon Amir, Itai Benjamini, Ori Gurel-Gurevich and Gady Kozma

Stochastic Processes and their Applications, 2020, vol. 130, issue 12, 7463-7482

Abstract: We introduce the notion of Random Walk in Changing Environment (RWCE) — a random walk on a weighted graph in which the weights may change between steps. RWCE’s generalize many known RW (e.g. reinforced RW, true SAW). We explore possible properties of RWCE’s, and provide criteria for recurrence and transience when the underlying graph is N or a tree. We construct a RWCE on Z2 where conductances can only change from 1 to 2 (once) but nevertheless the walk is transient, and conjecture that such behavior cannot happen when the changes do not depend on the location of the RWCE.

Date: 2020
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DOI: 10.1016/j.spa.2020.08.003

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