论文标题
关键集群级联
Critical cluster cascades
论文作者
论文摘要
我们考虑了$ \ mathbb {r}^d $上的一系列Poisson cluster点的过程：在\ mathbb {n} _0 _0 $ in step $ n \ in poist Postion上，构造的构建中心具有强度$ c/（n+1）$，对于某些$ c> 0 $，每个群集都由$ n $ n cypers compert $ n组成，我们均包含一个$ n $ n $ n $ n的份额。群集级联的收敛弱，并且限点过程等于空隙过程（灭绝），或者其强度$ c $与关键集群级联（持久性）相同。我们才能获得持久性，并且仅当且仅当棕榈版本的棕榈版随机步行是本地A.S.有限。这一结果使我们可以为持续的关键集群级联反应提供众多示例。
We consider a sequence of Poisson cluster point processes on $\mathbb{R}^d$: at step $n\in\mathbb{N}_0$ of the construction, the cluster centers have intensity $c/(n+1)$ for some $c>0$, and each cluster consists of the particles of a branching random walk up to generation $n$ generated by a point process with mean 1. We show that this 'critical cluster cascade' converges weakly, and that either the limit point process equals the void process (extinction), or it has the same intensity $c$ as the critical cluster cascade (persistence). We obtain persistence, if and only if the Palm version of the outgrown critical branching random walk is locally a.s. finite. This result allows us to give numerous examples for persistent critical cluster cascades.
