Survival of contact processes on the hierarchical group

0342729 - ÚTIA 2011 RIV DE eng J - Journal Article
Athreya, S.R. - Swart, Jan M.
Survival of contact processes on the hierarchical group.
Probability Theory and Related Fields. Roč. 147, č. 3 (2010), s. 529-563. ISSN 0178-8051. E-ISSN 1432-2064
R&D Projects: GA ČR GA201/06/1323
Institutional research plan: CEZ:AV0Z10750506
Keywords : contact process * survival * hierarchical group * coupling * renormalization group
Subject RIV: BA - General Mathematics
Impact factor: 1.590, year: 2010
http://library.utia.cas.cz/separaty/2010/SI/swart-0342729.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0185384