uu.seUppsala University Publications

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Random cover times using the Poisson cylinder process.PrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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(English)In: Latin American Journal of Probability and Mathematical Statistics, ISSN 1980-0436, E-ISSN 1980-0436Article in journal (Refereed) Accepted
##### Abstract [en]

##### Keywords [en]

Cover times, Poisson cylinder process
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-392502OAI: oai:DiVA.org:uu-392502DiVA, id: diva2:1348721
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt1124",{id:"formSmash:j_idt1124",widgetVar:"widget_formSmash_j_idt1124",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt1130",{id:"formSmash:j_idt1130",widgetVar:"widget_formSmash_j_idt1130",multiple:true}); Available from: 2019-09-05 Created: 2019-09-05 Last updated: 2019-09-05
##### In thesis

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 subset A of the d-dimensional Euclidean space. 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.

1. Selected Topics in Continuum Percolation: Phase Transitions, Cover Times and Random Fractals$(function(){PrimeFaces.cw("OverlayPanel","overlay1348901",{id:"formSmash:j_idt1404:0:j_idt1408",widgetVar:"overlay1348901",target:"formSmash:j_idt1404:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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