Central limit theorem for branching random walks in random environment
Central limit theorem for branching random walks in random environment
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DOI：
10.1214/07-aap500
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发表时间：
2007-12
影响因子：
1.8
通讯作者：
N. Yoshida
中科院分区：
文献类型：
--
作者：
N. Yoshida
研究了d维整数格上具有时空独立同分布的分支随机游动。后代分布当$d \ge 3$和环境的波动是很好地缓和的随机游走，我们证明了人口密度的中心极限定理，以及人口最多的网站和副本重叠的密度的上界。我们还讨论了该模型在无规环境中与定向聚合物有关的相变。
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. When $d \ge 3$ and the fluctuation of the environment is well moderated by the random walk, we prove a central limit theorem for the density of the population, together with upper bounds for the density of the most populated site and the replica overlap. We also discuss the phase transition of this model in connection with directed polymers in random environment.