Martingale defocusing and transience of a self-interacting random walk
Accepted version
Peer-reviewed
Repository URI
Repository DOI
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