Random cover times using the Poisson cylinder process
Journal article, 2019

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 cylinders to cover a set A subset of R-d . This Poisson process of cylinders is invariant under rotations, reflections and translations, and in addition we add a time component so that cylinders are "raining from the sky" at unit rate. Our main results concerns the asymptotic of this cover time as the set A grows. If the set A is discrete and well separated, we show convergence of the cover time to a Gumbel distribution. If instead A has positive box dimension (and satisfies a weak additional assumption), we find the correct rate of convergence.

Poisson cylinder process

Cover times


Erik Broman

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Filipe Mussini

Uppsala University


1980-0436 (ISSN)

Vol. 16 2 1165-1199

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis


Basic sciences



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