engleski

CLT for the capacity of the range of stable random walks

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 $d /\alpha> 5 /2$. 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.

capacity ; central limit theorem ; strong transience ; the range of a random walk

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