On central limit theorems in stochastic geometry

TL;DR

This paper proves central limit theorems for functionals of binomial and Poisson point processes, with an application to Betti numbers of random geometric complexes in large-scale regimes.

Contribution

It introduces new CLTs for general functionals on point processes and applies them to topological invariants in stochastic geometry.

Findings

CLTs established for binomial and Poisson point process functionals

Application to Betti numbers of random geometric complexes

Results applicable in thermodynamic limit regimes

Abstract

We establish central limit theorems for general functionals on binomial point processes and their Poissonized version. As an application, a central limit theorem for Betti numbers of random geometric complexes in the thermodynamic regime is derived.