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

Department of Mathematics

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

2 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

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

Funding

The research of G.A. was supported by the Israel Science Foundation grant ISF 1471/11 and by a grant from the GIF, the German-Israeli Foundation for Scientific Research and Development . The research of O.G.G. was supported by the Israel Science Foundation grant ISF 1707/16 .

Funders	Funder number
German-Israeli Foundation for Scientific Research and Development	ISF 1707/16
Israel Science Foundation	ISF 1471/11

Access to Document

10.1016/j.spa.2020.08.003

Cite this

@article{139f333c04d14070940e795bf944174a,

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.",

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

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

year = "2020",

month = dec,

doi = "10.1016/j.spa.2020.08.003",

language = "אנגלית",

volume = "130",

pages = "7463--7482",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier B.V.",

number = "12",

}

TY - JOUR

T1 - Random walk in changing environment

AU - Amir, Gideon

AU - Benjamini, Itai

AU - Gurel-Gurevich, Ori

AU - Kozma, Gady

PY - 2020/12

Y1 - 2020/12

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85090479625&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2020.08.003

DO - 10.1016/j.spa.2020.08.003

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85090479625

SN - 0304-4149

VL - 130

SP - 7463

EP - 7482

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 12

ER -

Random walk in changing environment

Abstract

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this