65th ISI World Statistics Congress

65th ISI World Statistics Congress

Quantitative normal approximations in the convex distance, with applications to coverage processes

Conference

65th ISI World Statistics Congress

Format: IPS Abstract - WSC 2025

Session: IPS 853 - Stein's Method and Stochastic Geometry

Monday 6 October 10:50 a.m. - 12:30 p.m. (Europe/Amsterdam)

Abstract

I will discuss a recent collection of probabilistic inequalities, providing upper bounds on the convex distance between the distribution of a Gaussian target and that of a random variable depending on a finite sample of independent random elements. We will discuss some applications of a geometric nature, notably to the fluctuations of intrinsic volumes associated with coverage processes (Boolean models) on Euclidean spaces. Based on the following joint work with M. Kasprzak:

M. J. Kasprzak and G. Peccati (2023). Vector-valued statistics of binomial processes: Berry-Esseen bounds in the convex distance. Ann. Appl. Probab. 33, No. 5, 3449-3492