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arXiv · 1009.0741

A balanced excited random walk

Itai Benjamini·Gady Kozma·Bruno Schapira
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Abstract

The following random process on $\Z^4$ is studied. At first visit to a site, the two first coordinates perform a (2-dimensional) simple random walk step. At further visits, it is the last two coordinates which perform a simple random walk step. We prove that this process is almost surely transient. The lower dimensional versions are discussed and various generalizations and related questions are proposed.

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Itai Benjamini, Gady Kozma, Bruno Schapira. 2010-09-03. A balanced excited random walk. https://arxiv.org/abs/1009.0741

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