Interlacement percolation on transient weighted graphs

Details Interlacement percolation on transient weighted graphs Interlacement percolation on transient weighted graphs

2009-07-02

arxiv.org/abs/0907.0316v1

Mathematics

Probability

25 pages, 2 figures, accepted for publication in the Elect. Journal of Prob

Scientific paper

In this article, we first extend the construction of random interlacements, introduced by A.S. Sznitman in [arXiv:0704.2560], 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 G satisfies the isoperimetric inequality IS_6 (see (1.5)), u_* is positive for the product GxZ (where we endow 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_*.

Affiliated with

Also associated with

No associations

Rating

Interlacement percolation on transient weighted graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Interlacement percolation on transient weighted graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Interlacement percolation on transient weighted graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-730719