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Bernoulli and self-destructive percolation on non-amenable graphs


 
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1. Title Title of document Bernoulli and self-destructive percolation on non-amenable graphs
 
2. Creator Author's name, affiliation, country Daniel Ahlberg; IMPA; Brazil
 
2. Creator Author's name, affiliation, country Vladas Sidoravicius; IMPA
 
2. Creator Author's name, affiliation, country Johan Tykesson; IMPA; Brazil
 
3. Subject Discipline(s)
 
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4. Description Abstract

In this note we study some properties of infinite percolation clusters on non-amenable graphs. In particular, we study the percolative properties of the complement  of infinite percolation clusters. An approach based on mass-transport is adapted to show that for a large class of non-amenable graphs, the graph obtained by removing each site contained in an infinite percolation cluster has critical percolation threshold which can be arbitrarily close to the critical threshold for the original graph, almost surely, as $p\searrow p_c$. Closely related is the self-destructive percolation process, introduced by J. van den Berg and R. Brouwer, for which we prove that an infinite cluster emerges for any small reinforcement.
 
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7. Date (YYYY-MM-DD) 2014-07-12
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2611
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-2611
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
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