5 Maggio, 2017 10:30 in punto

Sezione di Probabilità e Statistica Matematica

Invariance under quasi-isometries of subcritical and supercritical behavior in the Boolean model of percolation

Cristian Coletti, Universidade Federal do ABC, Santo André - Sao Paulo, Brasil

Aula seminari del III piano del Dipartimento di Matematica del Politecnico di Milano

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 the same does the Poisson Boolean model of percolation in N. We use these results in order to understand the phase transition phenomenon in a large family of metric spaces.