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Statements

Subject Item
n2:RIV%2F67985556%3A_____%2F10%3A00342729%21RIV11-GA0-67985556
rdf:type
n11:Vysledek skos:Concept
dcterms:description
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. 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.
dcterms:title
Survival of contact processes on the hierarchical group Survival of contact processes on the hierarchical group
skos:prefLabel
Survival of contact processes on the hierarchical group Survival of contact processes on the hierarchical group
skos:notation
RIV/67985556:_____/10:00342729!RIV11-GA0-67985556
n4:aktivita
n5:Z n5:P
n4:aktivity
P(GA201/06/1323), Z(AV0Z10750506)
n4:cisloPeriodika
3
n4:dodaniDat
n10:2011
n4:domaciTvurceVysledku
n13:1815350
n4:druhVysledku
n16:J
n4:duvernostUdaju
n17:S
n4:entitaPredkladatele
n18:predkladatel
n4:idSjednocenehoVysledku
291201
n4:idVysledku
RIV/67985556:_____/10:00342729
n4:jazykVysledku
n12:eng
n4:klicovaSlova
contact process; survival; hierarchical group; coupling; renormalization group
n4:klicoveSlovo
n7:contact%20process n7:renormalization%20group n7:hierarchical%20group n7:survival n7:coupling
n4:kodStatuVydavatele
DE - Spolková republika Německo
n4:kontrolniKodProRIV
[8F24D3F1C181]
n4:nazevZdroje
Probability Theory and Related Fields
n4:obor
n8:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
2
n4:projekt
n15:GA201%2F06%2F1323
n4:rokUplatneniVysledku
n10:2010
n4:svazekPeriodika
147
n4:tvurceVysledku
Swart, Jan M. Athreya, S. R.
n4:wos
000277028200005
n4:zamer
n9:AV0Z10750506
s:issn
0178-8051
s:numberOfPages
35