
Open access
Author
Date
2009Type
- Journal Article
Citations
Cited 42 times in
Web of Science
Cited 40 times in
Scopus
ETH Bibliography
yes
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Abstract
In this article, we first extend the construction of random interlacements, introduced by A.S. Sznitman in [14], to the more general setting of transient weighted graphs. We prove the Harris-FKG inequality for this model and analyze some of its properties on specific classes of graphs. For the case of non-amenable graphs, we prove that the critical value u∗ for the percolation of the vacant set is finite. We also prove that, once G satisfies the isoperimetric inequality IS6 (see (1.5)), u∗ is positive for the product G×Z (where we endow Z with unit weights). When the graph under consideration is a tree, we are able to characterize the vacant cluster containing some fixed point in terms of a Bernoulli independent percolation process. For the specific case of regular trees, we obtain an explicit formula for the critical value u∗. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000015442Publication status
publishedExternal links
Journal / series
Electronic Journal of ProbabilityVolume
Pages / Article No.
Publisher
Institute of Mathematical StatisticsSubject
random walks; random interlacements; percolationOrganisational unit
03320 - Sznitman, Alain-Sol (emeritus) / Sznitman, Alain-Sol (emeritus)
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Citations
Cited 42 times in
Web of Science
Cited 40 times in
Scopus
ETH Bibliography
yes
Altmetrics