CLT for the capacity of the range of stable random walks

11 Apr 2019  ·  Wojciech Cygan, Nikola Sandrić, Stjepan Šebek ·

In this article, we establish a central limit theorem for the capacity of the range process for a class of $d$-dimensional symmetric $\alpha$-stable random walks with the index satisfying $d > 5\alpha /2$. 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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Probability 60F05, 60G50, 60G52