Title: Functional CLTs for Local Statistics of Dynamic Point Processes.
Abstract: We will present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in the Euclidian space. The dynamics we study are those of a Markov birth-death process. We prove functional limit theorems in the so-called thermodynamic regime using the recent theory of Malliavin-Stein bounds. Our results are applicable to several functionals of interest in the stochastic geometry literature, including subgraph and component counts in the random geometric graphs. Our recent work extending these results to mobile points will also be discussed (Joint work with Omer Bobrowski and Robert J. Adler).