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Interlacement percolation on transient weighted graphs


 
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1. Title Title of document Interlacement percolation on transient weighted graphs
 
2. Creator Author's name, affiliation, country Augusto Teixeira; Eidgenössische Technische Hochschule Zürich
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random walks, random interlacements, percolation
 
3. Subject Subject classification 60K35, 82C41
 
4. Description 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 $\mathcal{G}$ satisfies the isoperimetric inequality $I S_6$ (see (1.5)), $u_*$ is positive for the product $\mathcal{G} \times \mathbb{Z}$ (where we endow $\mathbb{Z}$ 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 $u_*$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Swiss National Fund
 
7. Date (YYYY-MM-DD) 2009-07-09
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/670
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-670
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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