论文标题
在非本地竞争中进行随机步行
Branching random walk with non-local competition
论文作者
论文摘要
我们研究了较大的人口密度制度中种群动态的Bolker-Pacala-Dieckmann-law（BPDL）模型。 BPDL模型是一个粒子系统，其中粒子在空间中随机移动并在本地互相竞争。当人口密度足够大时，我们严格地证明了全球生存以及描述人口渐近扩散的形状定理。与大多数以前的研究相反，我们允许竞争内核具有任意的，甚至是无限的范围，从而术语非本地竞争。这使得粒子系统非符号酮和无限范围的依赖性，这意味着通常的比较参数分解，必须用更动手的方法代替。证明中的某些想法的灵感来自非本地Fisher-KPP方程的作品，但是模型的随机性会带来新的困难。
We study the Bolker-Pacala-Dieckmann-Law (BPDL) model of population dynamics in the regime of large population density. The BPDL model is a particle system in which particles reproduce, move randomly in space, and compete with each other locally. We rigorously prove global survival as well as a shape theorem describing the asymptotic spread of the population, when the population density is sufficiently large. In contrast to most previous studies, we allow the competition kernel to have an arbitrary, even infinite range, whence the term non-local competition. This makes the particle system non-monotone and of infinite-range dependence, meaning that the usual comparison arguments break down and have to be replaced by a more hands-on approach. Some ideas in the proof are inspired by works on the non-local Fisher-KPP equation, but the stochasticity of the model creates new difficulties.
