Martingale defocusing and transience of a self-interacting random walk

2014/03/06 by Peres, Yuval, Schapira, Bruno, Sousi, Perla · 1 citation
#60K35 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1403.1571

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.

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