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

Abstract

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.

References in corpus (1)

• Connectivity properties of random interlacement and intersection of random walks