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arXiv · 1807.02325

Deviations for the Capacity of the Range of a Random Walk

Amine Asselah·Bruno Schapira
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Abstract

We obtain estimates for large and moderate deviations for the capacity of the range of a random walk on $\mathbb{Z}^d$, in dimension $d\ge 5$, both in the upward and downward directions. The results are analogous to those we obtained for the volume of the range in two companion papers [AS17, AS19]. Interestingly, the main steps of the strategy we developed for the latter apply in this seemingly different setting, yet the details of the analysis are different

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Amine Asselah, Bruno Schapira. 2018-07-06. Deviations for the Capacity of the Range of a Random Walk. https://arxiv.org/abs/1807.02325

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