Growth rates of the population in a branching Brownian motion with an inhomogeneous breeding potential
Growth rates of the population in a branching Brownian motion with an inhomogeneous breeding potential
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DOI：
10.1016/j.spa.2014.12.008
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发表时间：
2012-03
影响因子：
1.4
通讯作者：
J. Berestycki;'Eric Brunet;J. Harris;S. Harris;Matthew I. Roberts
中科院分区：
文献类型：
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作者：
J. Berestycki;'Eric Brunet;J. Harris;S. Harris;Matthew I. Roberts
我们考虑一个分枝粒子系统，其中每个粒子作为独立的布朗运动运动，并以与其从原点到p次方的距离成正比的速度繁殖，对于p∈[0，2)。这个系统最右边的粒子的渐近行为是已知的；在本文中，我们给出了粒子沿着“困难”路径的大偏差概率，沿着“容易”路径的增长率，以及总的人口增长率，我们推导了粒子必须遵循的最优路径才能达到这个增长率。
We consider a branching particle system where each particle moves as an independent Brownian motion and breeds at a rate proportional to its distance from the origin raised to the power p, for p∈[0, 2). The asymptotic behaviour of the right-most particle for this system is already known; in this article we give large deviations probabilities for particles following “difficult” paths, growth rates along “easy” paths, the total population growth rate, and we derive the optimal paths which particles must follow to achieve this growth rate.