Capacity of the range of random walk on $\mathbb{Z}^d$

Amine Asselah, Bruno Schapira, Perla Sousi

Published 2016-02-10Version 1

We study the capacity of the range of a transient simple random walk on $\mathbb{Z}^d$. Our main result is a central limit theorem for the capacity of the range for $d\ge 6$. We present a few open questions in lower dimensions.