Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 19 (2014), paper no. 40, 6 pp.
Bernoulli and self-destructive percolation on non-amenable graphs
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.
Electron. Commun. Probab., Volume 19 (2014), paper no. 40, 6 pp.
Accepted: 12 July 2014
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
This work is licensed under a Creative Commons Attribution 3.0 License.
Ahlberg, Daniel; Sidoravicius, Vladas; Tykesson, Johan. Bernoulli and self-destructive percolation on non-amenable graphs. Electron. Commun. Probab. 19 (2014), paper no. 40, 6 pp. doi:10.1214/ECP.v19-2611. https://projecteuclid.org/euclid.ecp/1465316742