论文标题
barycentric的布朗蜜蜂
Barycentric Brownian Bees
论文作者
论文摘要
我们为Brunet-Derrida粒子系统的Barycenter建立了一个不变性原理。该模型由$ n $颗粒进行二元分支布朗尼运动，费率为$ 1 $。在分支事件中，通过删除远离barycenter的粒子，保持颗粒的数量等于$ n $。为了证明不变性原则，一个关键步骤是为从其重中心观看的过程建立哈里斯的复发。
We establish an invariance principle for the barycenter of a Brunet-Derrida particle system in $d$ dimensions. The model consists of $N$ particles undergoing dyadic branching Brownian motion with rate $1$. At a branching event, the number of particles is kept equal to $N$ by removing the particle located furthest away from the barycenter. To prove the invariance principle, a key step is to establish Harris recurrence for the process viewed from its barycenter.
