Functional Central Limit Theorems for Local Statistics of Spatial Birth-Death Processes in the Thermodynamic Regime

TL;DR

This paper establishes functional central limit theorems for local statistics of spatial birth-death processes, providing a process-level normal approximation in the thermodynamic regime, with applications to stochastic geometry.

Contribution

It introduces new functional limit theorems for local functionals of Markov birth-death processes in the thermodynamic regime, extending stochastic geometry analysis.

Findings

Proves process-level normal approximation for local functionals

Establishes functional limit theorems in the thermodynamic regime

Applicable to subgraph and component counts in random geometric graphs

Abstract

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.