Survival of contact processes on the hierarchical group

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F10%3A00342729" target="_blank" >RIV/67985556:_____/10:00342729 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Survival of contact processes on the hierarchical group
Original language 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 thehierarchical 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 andsurvival. 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F06%2F1323" target="_blank" >GA201/06/1323: Probabilistic methods in the study of phase transitions of complex systems</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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