论文标题
热力学状态中空间出生死亡过程局部局部统计的功能性中心限制定理
Functional Central Limit Theorems for Local Statistics of Spatial Birth-Death Processes in the Thermodynamic Regime
论文作者
论文摘要
我们在$ \ mathbb {r}^d $中定义的局部功能的过程级别上介绍了正常的近似结果。我们在这里研究的动态是马尔可夫出生死亡过程的动力。我们证明了所谓的热力学状态中的功能极限定理。我们的结果适用于随机几何文献中感兴趣的几个功能，包括随机几何图中的子图和组件计数。
We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in $\mathbb{R}^d$. The dynamics we study here are those of a Markov birth-death process. We prove functional limit theorems in the so-called thermodynamic regime. Our results are applicable to several functionals of interest in the stochastic geometry literature, including subgraph and component counts in the random geometric graphs.
