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Survival of Near-Critical Branching Brownian Motion

Abstract:

Consider a system of particles performing branching Brownian motion with negative drift, and killed upon hitting zero. Initially there is one particle at x > 0. Kesten (Stoch. Process. Appl. 7:9-47, 1978) showed that the process survives with positive probability if and only if ε > 0. Here we are interested in the asymptotics as ε→0 of the survival probability Qμ(x). It is proved that if, then for all x∈ℝ, lim ε→0Qμ(L+x)=θ(x)∈(0,1) exists and is a traveling wave solution of the Fisher-K...

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Publisher copy:
10.1007/s10955-011-0224-9

Authors


Berestycki, J More by this author
Berestycki, N More by this author
Schweinsberg, J More by this author
Journal:
Journal of Statistical Physics
Volume:
143
Issue:
5
Pages:
833-854
Publication date:
2011-06-05
DOI:
EISSN:
1572-9613
ISSN:
0022-4715
URN:
uuid:a41cafe9-40cc-47c9-9f2c-f1a1bf92144c
Source identifiers:
487697
Local pid:
pubs:487697

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