Survival of contact processes on the hierarchical group

Details Survival of contact processes on the hierarchical group Survival of contact processes on the hierarchical group

2008-08-27

arxiv.org/abs/0808.3732v3

Mathematics

Probability

Minor changes compared to previous version. Final version. 30 pages. 1 figure

Scientific paper

We consider contact processes on the hierarchical group, where sites infect other sites at a rate depending on their hierarchical distance, and sites become healthy with a constant recovery rate. If the infection rates decay too fast as a function of the hierarchical distance, then we show that the critical recovery rate is zero. On the other hand, we derive sufficient conditions on the speed of decay of the infection rates for the process to exhibit a nontrivial phase transition between extinction and survival. For our sufficient conditions, we use a coupling argument that compares contact processes on the hierarchical group with freedom two with contact processes on a renormalized lattice. An interesting novelty in this renormalization argument is the use of a result due to Rogers and Pitman on Markov functionals.

Affiliated with

Also associated with

No associations

Rating

Survival of contact processes on the hierarchical group 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 Survival of contact processes on the hierarchical group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Survival of contact processes on the hierarchical group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-529931