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Journal of Statistical Physics

, Volume 136, Issue 1, pp 145–163 | Cite as

Central Limit Theorem for Branching Brownian Motions in Random Environment

  • Yuichi Shiozawa
Article

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.

Keywords

Branching Brownian motion Random environment Poisson random measure Central limit theorem Phase transition Brownian directed polymer 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsKyoto UniversityKyotoJapan

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