A particle system with cooperative branching and coalescence

Kód výsledku v IS VaVaI

RIV/67985556:_____/15:00442871 - isvavai.cz

Výsledek na webu

http://dx.doi.org/10.1214/14-AAP1032

DOI - Digital Object Identifier

10.1214/14-AAP1032

Jazyk výsledku

angličtina

Název v původním jazyce

A particle system with cooperative branching and coalescence

Popis výsledku v původním jazyce

In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching") and particles that land on an occupied site merge with the particle present on that site ("coalescence"). We show that the system undergoes a phase transition as the branching rate is increased. For small branching rates the upper invariant law is trivial and the process started with finitely many particles a.s. ends up with asingle particle. Both statements are not true for high branching rates. An interesting feature of the process is that the spectral gap is zero even for low branching rates. Indeed, if the branching rate is small enough, then we show that for the processstarted in the fully occupied state, the particle density decays as one over the square root of time, and the same is true for the decay of the probability that the process still has more than one particle at a later time if it started w

Název v anglickém jazyce

A particle system with cooperative branching and coalescence

Popis výsledku anglicky

In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching") and particles that land on an occupied site merge with the particle present on that site ("coalescence"). We show that the system undergoes a phase transition as the branching rate is increased. For small branching rates the upper invariant law is trivial and the process started with finitely many particles a.s. ends up with asingle particle. Both statements are not true for high branching rates. An interesting feature of the process is that the spectral gap is zero even for low branching rates. Indeed, if the branching rate is small enough, then we show that for the processstarted in the fully occupied state, the particle density decays as one over the square root of time, and the same is true for the decay of the probability that the process still has more than one particle at a later time if it started w

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

GAP201/10/0752: Stochastické časoprostorové systémy

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Annals of Applied Probability

ISSN

1050-5164

e-ISSN

—

Svazek periodika

25

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

34

Strana od-do

1616-1649

Kód UT WoS článku

000353527000015

EID výsledku v databázi Scopus

2-s2.0-84925451822