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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Invariance Under Quasi-isometries of Subcritical and Supercritical Behavior in the Boolean Model of Percolation

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Coletti, Cristian F. [1] ; Miranda, Daniel [1] ; Mussini, Filipe [2]
Total Authors: 3
[1] Univ Fed ABC, Sao Paulo - Brazil
[2] Uppsala Univ, Uppsala - Sweden
Total Affiliations: 2
Document type: Journal article
Source: Journal of Statistical Physics; v. 162, n. 3, p. 685-700, FEB 2016.
Web of Science Citations: 0

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. (AU)

FAPESP's process: 12/24086-9 - Invariance under quasi-isometries of sub and supercritical behavior in Boolean percolation
Grantee:Filipe Biason Mussini
Support type: Scholarships in Brazil - Master
FAPESP's process: 09/52379-8 - Stochastic modeling of interacting systems
Grantee:Fabio Prates Machado
Support type: Research Projects - Thematic Grants