论文标题
无限蜂群中的布朗蜜蜂
Brownian bees in the infinite swarm limit
论文作者
论文摘要
布朗蜜蜂模型是具有空间选择的分支粒子系统。它是一个$ n $颗粒的系统，它以$ \ mathbb {r}^d $中的独立布朗运动作为独立的动作，并以速率1独立分支，至关重要的是，在每个分支事件中，距离原点最远的粒子被删除以保持人口大小的恒定。在目前的工作中，我们证明，作为$ n \ to \ infty $，粒子系统的行为通过自由边界问题的解决方案（这是伴侣纸的主题），即系统的流体动力极限。然后，我们证明，对于此模型，所谓的选择原理保留，即作为$ n \至\ infty $，粒子系统的平衡密度会收敛到自由边界问题的稳态解决方案。
The Brownian bees model is a branching particle system with spatial selection. It is a system of $N$ particles which move as independent Brownian motions in $\mathbb{R}^d$ and independently branch at rate 1, and, crucially, at each branching event, the particle which is the furthest away from the origin is removed to keep the population size constant. In the present work we prove that as $N \to \infty$ the behaviour of the particle system is well approximated by the solution of a free boundary problem (which is the subject of a companion paper), the hydrodynamic limit of the system. We then show that for this model the so-called selection principle holds, i.e. that as $N \to \infty$ the equilibrium density of the particle system converges to the steady state solution of the free boundary problem.
