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Percolation and isoperimetry on roughly transitive graphs
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Candellero, Elisabetta and Teixeira, Augusto (2018) Percolation and isoperimetry on roughly transitive graphs. Annales de l’Institut Henri Poincaré - Probabilites et Statistiques, 54 (4). pp. 1819-1847. doi:10.1214/17-AIHP857 ISSN 0246-0203.
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Official URL: https://doi.org/10.1214/17-AIHP857
Abstract
In this paper we study percolation on a roughly transitive graph G with polynomial growth and isoperimetric dimension larger than one. For these graphs we are able to prove that pc < 1, or in other words, that there exists a percolation phase. The main results of the article work for both dependent and independent percolation processes, since they are based on a quite robust renormalization technique. When G is transitive, the fact that pc < 1 was already known before. But even in that case our proof yields some new results and it is entirely probabilistic, not involving the use of Gromov’s theorem on groups of polynomial growth. We finish the paper giving some examples of dependent percolation for which our results apply.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Library of Congress Subject Headings (LCSH): | Graph theory, Percolation (Statistical physics) | ||||||
Journal or Publication Title: | Annales de l’Institut Henri Poincaré - Probabilites et Statistiques | ||||||
Publisher: | Institute of Mathematical Statistics | ||||||
ISSN: | 0246-0203 | ||||||
Official Date: | 18 October 2018 | ||||||
Dates: |
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Volume: | 54 | ||||||
Number: | 4 | ||||||
Page Range: | pp. 1819-1847 | ||||||
DOI: | 10.1214/17-AIHP857 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 2 August 2017 | ||||||
Date of first compliant Open Access: | 9 January 2019 | ||||||
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