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A particle system with cooperative branching and coalescence

SYSNO ASEP	0442871
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	A particle system with cooperative branching and coalescence
Author(s)	Sturm, A. (DE) Swart, Jan M. (UTIA-B)_{RID, ORCID}
Number of authors	2
Source Title	Annals of Applied Probability. - : Institute of Mathematical Statistics - ISSN 1050-5164 Roč. 25, č. 3 (2015), s. 1616-1649
Number of pages	34 s.
Publication form	Print - P
Language	eng - English
Country	US - United States
Keywords	interacting particle system ; cooperative branching ; coalescence ; phase transition ; upper invariant law ; survival ; extinction
Subject RIV	BA - General Mathematics
R&D Projects	GAP201/10/0752 GA ČR - Czech Science Foundation (CSF)
Institutional support	UTIA-B - RVO:67985556
UT WOS	000353527000015
EID SCOPUS	84925451822
DOI	10.1214/14-AAP1032
Annotation	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 a single 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 process started 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 with two particles.
Workplace	Institute of Information Theory and Automation
Contact	Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201.
Year of Publishing	2016

Number of the records: 1