Invariance Under Quasi-isometries of Subcritical and Supercritical Behavior in the Boolean Model of Percolation
2016 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 162, no 3, 685-700 p.Article in journal (Refereed) PublishedText
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.
Place, publisher, year, edition, pages
2016. Vol. 162, no 3, 685-700 p.
Poisson point process, Percolation, Boolean model, Quasi-isometries
IdentifiersURN: urn:nbn:se:uu:diva-282329DOI: 10.1007/s10955-015-1422-7ISI: 000371086600006OAI: oai:DiVA.org:uu-282329DiVA: diva2:916831