Subcritical contact processes seen from a typical infected site

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F14%3A00429073" target="_blank" >RIV/67985556:_____/14:00429073 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1214/EJP.v19-2904" target="_blank" >http://dx.doi.org/10.1214/EJP.v19-2904</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1214/EJP.v19-2904" target="_blank" >10.1214/EJP.v19-2904</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Subcritical contact processes seen from a typical infected site

Popis výsledku v původním jazyce

What is the long-time behavior of the law of a contact process started with a single infected site, distributed according to counting measure on the lattice? This question is related to the configuration as seen from a typical infected site and gives rise to the definition of so-called eigenmeasures, which are possibly infinite measures on the set of nonempty configurations that are preserved under the dynamics up to a time-dependent exponential factor. In this paper, we study eigenmeasures of contact processes on general countable groups in the subcritical regime. We prove that in this regime, the process has a unique spatially homogeneous eigenmeasure. As an application, we show that the law of the process as seen from a typical infected site, chosenaccording to a Campbell law, converges to a long-time limit.

Název v anglickém jazyce

Subcritical contact processes seen from a typical infected site

Popis výsledku anglicky

What is the long-time behavior of the law of a contact process started with a single infected site, distributed according to counting measure on the lattice? This question is related to the configuration as seen from a typical infected site and gives rise to the definition of so-called eigenmeasures, which are possibly infinite measures on the set of nonempty configurations that are preserved under the dynamics up to a time-dependent exponential factor. In this paper, we study eigenmeasures of contact processes on general countable groups in the subcritical regime. We prove that in this regime, the process has a unique spatially homogeneous eigenmeasure. As an application, we show that the law of the process as seen from a typical infected site, chosenaccording to a Campbell law, converges to a long-time limit.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Electronic Journal of Probability

ISSN

1083-6489

e-ISSN

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Svazek periodika

19

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

46

Strana od-do

53-1-53-46

Kód UT WoS článku

000341096600001

EID výsledku v databázi Scopus

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