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

Nathakhun Wiroonsri

doi:10.1016/j.jmaa.2019.123396

paper

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

arXiv:1903.04116 · doi:10.1016/j.jmaa.2019.123396

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 $α$ -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.

20 pages