Excited Mob

Gideon Amir; Tal Orenshtein

doi:10.1016/j.spa.2015.09.007

Excited Mob

Gideon Amir, Tal Orenshtein

Department of Mathematics

Universite Claude Bernard Lyon 1

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

3 Scopus citations

Abstract

We study one dimensional excited random walks (ERW) on iterated leftover environments. We prove a 0-1 law for directional transience and a law of large numbers for such environments under mild assumptions. We provide exact criteria for transience and positive speed of the walk in terms of the expected drift per site under stronger assumptions. This allows us to construct examples of stationary and ergodic environments on which ERW has positive speed that do not follow by trivial comparison to i.i.d. environments. A central ingredient is the introduction of the "Excited Mob" of k walkers on the same cookie environment.

Original language	English
Pages (from-to)	439-469
Number of pages	31
Journal	Stochastic Processes and their Applications
Volume	126
Issue number	2
DOIs	https://doi.org/10.1016/j.spa.2015.09.007
State	Published - 1 Feb 2016

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V. 2015 Elsevier B.V. All rights reserved.

Funding

We thank Noam Berger and Gady Kozma for useful discussions. We thank the anonymous referees for their thorough reading of the earlier version of this manuscript and their useful comments which helped to improve this paper. The research of G.A. was supported by the Israel Science Foundation grant ISF 1471/11 and by a young GIF grant from the German Israeli foundation . The research of T.O. was partly supported by the Israel Science Foundation.

Funders	Funder number
German Israeli Foundation
Israel Science Foundation	ISF 1471/11

Keywords

Abelianness
Cookie walk
Excited random walk
Law of large numbers
Limit theorems
Random environment
Recurrence
Regeneration structure
Transience
Zero one laws

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10.1016/j.spa.2015.09.007

Cite this

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KW - Cookie walk

KW - Excited random walk

KW - Law of large numbers

KW - Limit theorems

KW - Random environment

KW - Recurrence

KW - Regeneration structure

KW - Transience

KW - Zero one laws

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Excited Mob

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Bibliographical note

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Keywords

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