Capacity of the range of random walk on $\mathbb{Z}^4$

Amine Asselah; Bruno Schapira; Perla Sousi

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arXiv · 1611.04567

Capacity of the range of random walk on $\mathbb{Z}^4$

Amine Asselah·Bruno Schapira·Perla Sousi

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Abstract

We study the scaling limit of the capacity of the range of a simple random walk on the integer lattice in dimension four. We establish a strong law of large numbers and a central limit theorem with a non-gaussian limit. The asymptotic behaviour is analogous to that found by Le Gall in '86 for the volume of the range in dimension two.

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Amine Asselah, Bruno Schapira, Perla Sousi. 2016-11-14. Capacity of the range of random walk on $\mathbb{Z}^4$. https://arxiv.org/abs/1611.04567

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