| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [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 |
| Abstract | |
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 |