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arXiv · 1507.01031

Boundary of the Range of Transient Random Walk

Amine Asselah·Bruno Schapira
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Abstract

We study the boundary of the range of simple random walk on $\mathbb{Z}^d$ in the transient regime $d\ge 3$. We show that volumes of the range and its boundary differ mainly by a martingale. As a consequence, we obtain a bound on the variance of order $n\log n$ in dimension three. We also establish a central limit theorem in dimension four and larger.

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Amine Asselah, Bruno Schapira. 2015-07-03. Boundary of the Range of Transient Random Walk. https://arxiv.org/abs/1507.01031

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