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2021 Localization at the boundary for conditioned random walks in random environment in dimensions two and higher
Rodrigo Bazaes
Author Affiliations +
Electron. Commun. Probab. 26: 1-13 (2021). DOI: 10.1214/21-ECP426

Abstract

We introduce the notion of localization at the boundary for conditioned random walks in i.i.d. and uniformly elliptic random environment on Zd, in dimensions two and higher. If d=2 or 3, we prove localization for (almost) all walks. In contrast, for d4, there is a phase transition for environments of the form ωε(x,e)=α(e)(1+εξ(x,e)), where {ξ(x)}xZd is an i.i.d. sequence of random variables, and ε represents the amount of disorder with respect to a simple random walk.

Funding Statement

The author has been supported by ANID-PFCHA/Doctorado Nacional/2018-21180873.

Acknowledgments

The author thanks his advisor Alejandro F. Ramírez and an anonymous referee for valuable comments and suggestions about the paper. Also, the author is grateful to Gregorio Moreno for a couple of discussions and bibliographical remarks.

Citation

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Rodrigo Bazaes. "Localization at the boundary for conditioned random walks in random environment in dimensions two and higher." Electron. Commun. Probab. 26 1 - 13, 2021. https://doi.org/10.1214/21-ECP426

Information

Received: 21 February 2021; Accepted: 4 September 2021; Published: 2021
First available in Project Euclid: 27 September 2021

arXiv: 1911.06430
Digital Object Identifier: 10.1214/21-ECP426

Subjects:
Primary: 60K37 , 82C41 , 82D30

Keywords: Localization , random environment , Random walks

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