Abstract We introduce and examine a class of stochastic spatial point processes with births and deaths, related to spatial loss networks introduced in Ferrari et al. In these processes, a point stays in the system until it is removed due to interaction with a conflicting new arrival. In particular, we consider an interaction scheme where two points are conflicting if closed balls of radius 1/2 around them overlap and a new arriving point “ kills” each conflicting point independently with probability ρ. The new point is accepted if all conflicting points are killed. We construct this process on the whole Euclidean space , . If ρ is large enough, we show existence of a stationary regime and exponential convergence to the stationary distribution. Such stochastic models have been studied earlier as models for populations of interacting individuals or as spatial queuing and resource sharing networks.

中文翻译：

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一个同时出生和死亡的硬核随机过程

摘要 我们介绍并研究了一类与出生和死亡的随机空间点过程，与 Ferrari 等人引入的空间损失网络相关。在这些过程中，一个点会一直留在系统中，直到它因与冲突的新到达者交互而被移除。特别地，我们考虑了一个交互方案，如果两个点周围半径为 1/2 的闭合球重叠，那么两个点就会发生冲突，并且一个新到达的点以概率 ρ 独立地“杀死”每个冲突点。如果所有冲突点都被杀死，则接受新点。我们在整个欧几里得空间上构造这个过程， 。如果 ρ 足够大，我们表明存在平稳状态并且指数收敛于平稳分布。