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

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.