A particle system with cooperative branching and coalescence
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F15%3A00442871" target="_blank" >RIV/67985556:_____/15:00442871 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1214/14-AAP1032" target="_blank" >http://dx.doi.org/10.1214/14-AAP1032</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1214/14-AAP1032" target="_blank" >10.1214/14-AAP1032</a>
Alternative languages
Result language
angličtina
Original language name
A particle system with cooperative branching and coalescence
Original language description
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
Czech name
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Czech description
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Classification
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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Result continuities
Project
<a href="/en/project/GAP201%2F10%2F0752" target="_blank" >GAP201/10/0752: Stochastic Space-Time Systems</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annals of Applied Probability
ISSN
1050-5164
e-ISSN
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Volume of the periodical
25
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
34
Pages from-to
1616-1649
UT code for WoS article
000353527000015
EID of the result in the Scopus database
2-s2.0-84925451822