Multivariate central limit theorems for Rademacher functionals with applications

摘要

Quantitative multivariate central limit theorems for general functionals ofpossibly non-symmetric and non-homogeneous infinite Rademacher sequences areproved by combining discrete Malliavin calculus with the smart path method fornormal approximation. In particular, a discrete multivariate second-orderPoincar\'e inequality is developed. As a first application, the normalapproximation of vectors of subgraph counting statistics in theErd\H{o}s-R\'enyi random graph is considered. In this context, we furtherspecialize to the normal approximation of vectors of vertex degrees. In asecond application we prove a quantitative multivariate central limit theoremfor vectors of intrinsic volumes induced by random cubical complexes.