Neighboring clusters at Bernoulli percolation

  • Date: 03/20/2008

Adam Timar (University of British Columbia)


University of British Columbia


The study of Bernoulli percolation on general infinite transitive
graphs was initiated by a paper of Benjamini and Schramm in 1996, and
has been intensive since then. One of the interesting phenomena is that
for certain graphs there is a value of p when there are infinitely many
infinite components. This is conjectured to be a characterizing
property of nonamenable graphs. Haggstrom, Peres and Schonmann asked
whether it can happen that two infinite components of such a
percolation come at distance 1 from each other at infinitely many
places. We give a negative answer to this question.

Other Information: 

Probability Seminar 2006