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