uu.seUppsala University Publications

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Invariance Under Quasi-isometries of Subcritical and Supercritical Behavior in the Boolean Model of PercolationPrimeFaces.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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2016 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 162, no 3, p. 685-700Article in journal (Refereed) Published
##### Resource type

Text
##### Abstract [en]

##### Place, publisher, year, edition, pages

2016. Vol. 162, no 3, p. 685-700
##### Keywords [en]

Poisson point process, Percolation, Boolean model, Quasi-isometries
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-282329DOI: 10.1007/s10955-015-1422-7ISI: 000371086600006OAI: oai:DiVA.org:uu-282329DiVA, id: diva2:916831
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##### In thesis

In this work we study the Poisson Boolean model of percolation in locally compact Polish metric spaces and we prove the invariance of subcritical and supercritical phases under mm-quasi-isometries. More precisely, we prove that if a metric space M is mm-quasi-isometric to another metric space N and the Poisson Boolean model in M exhibits any of the following: (a) a subcritical phase; (b) a supercritical phase; or (c) a phase transition, then respectively so does the Poisson Boolean model of percolation in N. Then we use these results in order to understand the phase transition phenomenon in a large family of metric spaces. Indeed, we study the Poisson Boolean model of percolation in the context of Riemannian manifolds, in a large family of nilpotent Lie groups and in Cayley graphs. Also, we prove the existence of a subcritical phase in Gromov spaces with bounded growth at some scale.

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});});

doi
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