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

Autor(es)

Coletti, Cristian F. ^[1] ; Miranda, Daniel ^[1] ; Mussini, Filipe ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed ABC, Sao Paulo - Brazil

^[2] Uppsala Univ, Uppsala - Sweden

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 162, n. 3, p. 685-700, FEB 2016.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 12/24086-9 - Invariância por quasi-isometrias dos comportamentos sub e supercríticos na percolação booleana
• Beneficiário: Filipe Biason Mussini
• Modalidade de apoio: Bolsas no Brasil - Mestrado
• Processo FAPESP: 09/52379-8 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático