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Central Limit Theorem for Branching Brownian Motions in Random Environment

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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.

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  1. Yuichi Shiozawa

    Present address: Graduate School of Natural Science and Technology, Okayama University, Okayama, 700-8530, Japan

Authors and Affiliations

  1. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

    Yuichi Shiozawa

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  1. Yuichi Shiozawa
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Correspondence to Yuichi Shiozawa.

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Partly supported by the Global COE program at Department of Mathematics and Research Institute for Mathematical Sciences, Kyoto University.

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Shiozawa, Y. Central Limit Theorem for Branching Brownian Motions in Random Environment. J Stat Phys 136, 145–163 (2009). https://doi.org/10.1007/s10955-009-9774-5

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  • DOI: https://doi.org/10.1007/s10955-009-9774-5

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