Capacity of the range of random walk on $\mathbb{Z}^4$
Probability
2016-12-30 v2
Abstract
We study the scaling limit of the capacity of the range of a simple random walk on the integer lattice in dimension four. We establish a strong law of large numbers and a central limit theorem with a non-gaussian limit. The asymptotic behaviour is analogous to that found by Le Gall in '86 for the volume of the range in dimension two.
Keywords
Cite
@article{arxiv.1611.04567,
title = {Capacity of the range of random walk on $\mathbb{Z}^4$},
author = {Amine Asselah and Bruno Schapira and Perla Sousi},
journal= {arXiv preprint arXiv:1611.04567},
year = {2016}
}