October 2023 Functional central limit theorems for local statistics of spatial birth–death processes in the thermodynamic regime
Efe Onaran, Omer Bobrowski, Robert J. Adler
Author Affiliations +
Ann. Appl. Probab. 33(5): 3958-3986 (October 2023). DOI: 10.1214/22-AAP1912

Abstract

We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in Rd. 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.

Funding Statement

EO was supported in part by the Israel Science Foundation, Grants 2539/17 and 1965/19.
OB was supported in part by the Israel Science Foundation, Grant 1965/19.
RJA was supported in part by the Israel Science Foundation, Grant 2539/17.

Acknowledgments

The authors are grateful to Yogeshwaran Dhandapani for useful discussions and advice, and in particular for pointing us in the direction of highly related literature. The authors would also like to thank the anonymous referee for a timely and detailed report, with valuable suggestions on how to improve the manuscript.

Citation

Download Citation

Efe Onaran. Omer Bobrowski. Robert J. Adler. "Functional central limit theorems for local statistics of spatial birth–death processes in the thermodynamic regime." Ann. Appl. Probab. 33 (5) 3958 - 3986, October 2023. https://doi.org/10.1214/22-AAP1912

Information

Received: 1 February 2022; Revised: 1 October 2022; Published: October 2023
First available in Project Euclid: 3 November 2023

Digital Object Identifier: 10.1214/22-AAP1912

Subjects:
Primary: 60F05 , 60G55
Secondary: 05C80 , 60D05

Keywords: functional central limit theorems , Ornstein–Uhlenbeck process , Random geometric graphs , spatial birth–death process

Rights: Copyright © 2023 Institute of Mathematical Statistics

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Vol.33 • No. 5 • October 2023
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