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arXiv · 1904.05695

CLT for the capacity of the range of stable random walks

Wojciech Cygan·Nikola Sandrić·Stjepan Šebek
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Abstract

In this article, we establish a central limit theorem for the capacity of the range process for a class of $d$-dimensional symmetric $α$-stable random walks with the index satisfying $d > 5α/2$. Our approach is based on controlling the limit behavior of the variance of the capacity of the range process which then allows us to apply the Lindeberg-Feller theorem.

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Wojciech Cygan, Nikola Sandrić, Stjepan Šebek. 2021-04-19. CLT for the capacity of the range of stable random walks. https://arxiv.org/abs/1904.05695

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