Abstract
We introduce a model of branching Brownian motions in time-space random environment associated with the Poisson random measure. We prove that, if the randomness of the environment is moderated by that of the Brownian motion, the population density satisfies a central limit theorem and the growth rate of the population size is the same as its expectation with strictly positive probability. We also characterize the diffusive behavior of our model in terms of the decay rate of the replica overlap. On the other hand, we show that, if the randomness of the environment is strong enough, the growth rate of the population size is strictly less than its expectation almost surely. To do this, we use a connection between our model and the model of Brownian directed polymers in random environment introduced by Comets and Yoshida.
| Original language | English |
|---|---|
| Pages (from-to) | 145-163 |
| Number of pages | 19 |
| Journal | Journal of Statistical Physics |
| Volume | 136 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jul 2009 |
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Keywords
- Branching Brownian motion
- Brownian directed polymer
- Central limit theorem
- Phase transition
- Poisson random measure
- Random environment
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
Central limit theorem for branching Brownian motions in random environment. / Shiozawa, Yuichi.
In: Journal of Statistical Physics, Vol. 136, No. 1, 07.2009, p. 145-163.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Central limit theorem for branching Brownian motions in random environment
AU - Shiozawa, Yuichi
PY - 2009/7
Y1 - 2009/7
N2 - We introduce a model of branching Brownian motions in time-space random environment associated with the Poisson random measure. We prove that, if the randomness of the environment is moderated by that of the Brownian motion, the population density satisfies a central limit theorem and the growth rate of the population size is the same as its expectation with strictly positive probability. We also characterize the diffusive behavior of our model in terms of the decay rate of the replica overlap. On the other hand, we show that, if the randomness of the environment is strong enough, the growth rate of the population size is strictly less than its expectation almost surely. To do this, we use a connection between our model and the model of Brownian directed polymers in random environment introduced by Comets and Yoshida.
AB - We introduce a model of branching Brownian motions in time-space random environment associated with the Poisson random measure. We prove that, if the randomness of the environment is moderated by that of the Brownian motion, the population density satisfies a central limit theorem and the growth rate of the population size is the same as its expectation with strictly positive probability. We also characterize the diffusive behavior of our model in terms of the decay rate of the replica overlap. On the other hand, we show that, if the randomness of the environment is strong enough, the growth rate of the population size is strictly less than its expectation almost surely. To do this, we use a connection between our model and the model of Brownian directed polymers in random environment introduced by Comets and Yoshida.
KW - Branching Brownian motion
KW - Brownian directed polymer
KW - Central limit theorem
KW - Phase transition
KW - Poisson random measure
KW - Random environment
UR - http://www.scopus.com/inward/record.url?scp=70349337345&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=70349337345&partnerID=8YFLogxK
U2 - 10.1007/s10955-009-9774-5
DO - 10.1007/s10955-009-9774-5
M3 - Article
AN - SCOPUS:70349337345
VL - 136
SP - 145
EP - 163
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 1
ER -