Central limit theorem for branching Brownian motions in random environment

Yuichi Shiozawa

Research output: Contribution to journalArticle

7 Citations (Scopus)

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 languageEnglish
Pages (from-to)145-163
Number of pages19
JournalJournal of Statistical Physics
Volume136
Issue number1
DOIs
Publication statusPublished - Jul 2009

Fingerprint

Branching Brownian Motion
Random Environment
Central limit theorem
theorems
Population Size
Randomness
Poisson Random Measure
Directed Polymers
Strictly positive
Replica
comets
replicas
Decay Rate
Model
decay rates
Brownian motion
Overlap
Strictly
Space-time
polymers

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 journalArticle

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