Bernoulli and self-destructive percolation on non-amenable graphs
Journal article, 2014

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 approaches 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.

Author

Daniel Ahlberg

Vladas Sidoravicius

Johan Tykesson

Electronic Communications in Probability

1083-589X (ISSN)

Vol. 19 article 40-

Roots

Basic sciences

Subject Categories

Probability Theory and Statistics

DOI

10.1214/ECP.v19-2611

More information

Created

10/10/2017