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arXiv · 1908.07872

Functional CLT for the range of stable random walks

Wojciech Cygan·Nikola Sandrić·Stjepan Šebek
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Abstract

In this note, we establish a functional central limit theorem for the capacity of the range for a class of $\alpha$-stable random walks on the integer lattice $\mathbb{Z}^d$ with $d > 5\alpha/2$. Using similar methods, we also prove an analogous result for the cardinality of the range when $d > 3\alpha / 2$.

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Wojciech Cygan, Nikola Sandrić, Stjepan Šebek. 2019-08-21. Functional CLT for the range of stable random walks. https://arxiv.org/abs/1908.07872

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