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In this article, we establish a central limit theorem for the capacity of therange process for a class of $d$-dimensional symmetric $\alpha$-stable randomwalks with the index satisfying $d > 5\alpha /2$. Our approach is based oncontrolling the limit behavior of the variance of the capacity of the rangeprocess which then allows us to apply the Lindeberg-Feller theorem.

CLT for the capacity of the range of stable random walks