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arXiv · 1709.04378

Random cover times using the Poisson cylinder process

Erik I. Broman·Filipe Mussini
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Abstract

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 $A \subset \mathbb{R}^d.$ 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.

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Erik I. Broman, Filipe Mussini. 2017-09-13. Random cover times using the Poisson cylinder process. https://arxiv.org/abs/1709.04378

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