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Martingale defocusing and transience of a self-interacting random walk

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Peres, Yuval 
Schapira, Bruno 
Sousi, Perla 

Abstract

Suppose that (X,Y,Z) is a random walk in Z3 that moves in the following way: on the first visit to a vertex only Z changes by ±1 equally likely, while on later visits to the same vertex (X,Y) performs a two-dimensional random walk step. We show that this walk is transient thus answering a question of Benjamini, Kozma and Schapira. One important ingredient of the proof is a dispersion result for martingales.

Description

Keywords

4901 Applied Mathematics, 49 Mathematical Sciences, 4905 Statistics

Journal Title

Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Conference Name

Journal ISSN

0246-0203

Volume Title

52

Publisher

Institute of Mathematical Statistics