Random walk in changing environment

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageAmerican English
Pages (from-to)7463-7482
Number of pages20
JournalStochastic Processes and their Applications
Volume130
Issue number12
DOIs
StatePublished - Dec 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

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