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 $d/\alpha >5/2$. Our approach is based on controlling the limit behaviour of the variance of the capacity of the range process which then allows us to apply the Lindeberg–Feller theorem.

中文翻译：

---

稳定随机游走范围容量的中心极限定理

在本文中，我们建立了一类d维对称α稳定随机游走的范围过程容量的中心极限定理，其指标满足$d/\alpha >5/2$. 我们的方法基于控制范围过程容量方差的极限行为，然后允许我们应用林德伯格-费勒定理。