Random walk in changing environment

Gideon Amir; Itai Benjamini; Ori Gurel-Gurevich; Gady Kozma

doi:10.1016/j.spa.2020.08.003

Random walk in changing environment

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

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 language	English
Pages (from-to)	7463-7482
Number of pages	20
Journal	Stochastic Processes and their Applications
Volume	130
Issue number	12
DOIs	https://doi.org/10.1016/j.spa.2020.08.003
State	Published - Dec 2020

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© 2020 Elsevier B.V.

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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.",

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AU - Kozma, Gady

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Random walk in changing environment

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