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

Bar-Ilan University, The Hebrew University of Jerusalem, Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	7463-7482
Number of pages	20
Journal	Stochastic Processes and their Applications
Volume	130
Issue number	12
Early online date	28 Aug 2020
DOIs	https://doi.org/10.1016/j.spa.2020.08.003
State	Published - Dec 2020

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1016/j.spa.2020.08.003

http://arxiv.org/abs/1504.04870License: Other

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title = "Random walk in changing environment",

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 - Gurel-Gurevich, Ori

AU - Kozma, Gady

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AB - 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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JF - Stochastic Processes and their Applications

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ER -

Random walk in changing environment

Abstract

ASJC Scopus subject areas

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