期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2019
卷号：XVI
期号：2
页码：1165-1199
DOI：10.30757/ALEA.v16-44
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：In this paper we deal with the classical problem of random cover times.We investigate the distribution of the time it takes for a Poisson process of cylindersto cover a set A Rd: This Poisson process of cylinders is invariant under rotations,reflections and translations, and in addition we add a time component so thatcylinders are “raining from the sky" at unit rate. Our main results concerns theasymptotic of this cover time as the set A grows. If the set A is discrete and wellseparated, we show convergence of the cover time to a Gumbel distribution. Ifinstead A has positive box dimension (and satisfies a weak additional assumption),we find the correct rate of convergence.
