Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation on quasi-transitive graphs

Details Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation on quasi-transitive graphs Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation on quasi-transitive graphs

2007-07-07

arxiv.org/abs/0707.1089v3

Mathematics

Probability

Latex 2e; 25 pages (a4wide); small editorial corrections; one reference added

Scientific paper

10.1007/s10955-007-9459-x

We study homogeneous, independent percolation on general quasi-transitive graphs. We prove that in the disorder regime where all clusters are finite almost surely, in fact the expectation of the cluster size is finite. This extends a well-known theorem by Menshikov and Aizenman & Barsky to all quasi-transitive graphs. Moreover we deduce that in this disorder regime the cluster size distribution decays exponentially, extending a result of Aizenman & Newman. Our results apply to both edge and site percolation, as well as long range (edge) percolation. The proof is based on a modification of the Aizenman & Barsky method.

Affiliated with

Also associated with

No associations

Rating

Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation on quasi-transitive 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 Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation on quasi-transitive graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation on quasi-transitive graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-702322