# Normal approximation for associated point processes via Stein's method with applications to determinantal point processes

## TL;DR

This paper develops a Stein's method-based approach to establish non-asymptotic normal approximation bounds for functionals of associated point processes, with applications to determinantal and Laguerre-Gaussian point processes.

## Contribution

It introduces a novel Stein's method framework for associated point processes, linking association with $eta$-mixing, and applies it to determinantal and Laguerre-Gaussian processes.

## Key findings

- Provides explicit $L^1$ bounds for normal approximation.
- Demonstrates applicability to determinantal point processes.
- Suggests potential for broader applications in related point processes.

## Abstract

We use Stein's method to provide non asymptotic $L^1$ bounds to the normal for functionals of associated point processes. As for supporting tools, we use the connection between association and $\alpha$-mixing properties that was recently uncovered by [PDL17]. We apply our main results to determinantal point processes which are known to be negatively associated. A potential application to point processes in the Laguerre-Gaussian family is also presented.