Deviations for the Capacity of the Range of a Random Walk
Probability
2020-05-20 v4
Abstract
We obtain estimates for large and moderate deviations for the capacity of the range of a random walk on , in dimension , both in the upward and downward directions. The results are analogous to those we obtained for the volume of the range in two companion papers [AS17, AS19]. Interestingly, the main steps of the strategy we developed for the latter apply in this seemingly different setting, yet the details of the analysis are different
Cite
@article{arxiv.1807.02325,
title = {Deviations for the Capacity of the Range of a Random Walk},
author = {Amine Asselah and Bruno Schapira},
journal= {arXiv preprint arXiv:1807.02325},
year = {2020}
}
Comments
This version covers the whole moderate deviation regime in $d\ge 7$