Cover levels and random interlacements
Probability
2012-07-25 v2
Abstract
This note investigates cover levels of finite sets in the random interlacements model introduced in [Ann. of Math. (2) 171 (2010) 2039-2087], that is, the least level such that the set is completely contained in the random interlacement at that level. It proves that as the cardinality of a set goes to infinity, the rescaled and recentered cover level tends in distribution to the Gumbel distribution with cumulative distribution function .
Cite
@article{arxiv.1103.2072,
title = {Cover levels and random interlacements},
author = {David Belius},
journal= {arXiv preprint arXiv:1103.2072},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AAP770 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)