Multivariate central limit theorems for Rademacher functionals with applications
Probability
2017-11-06 v1
Abstract
Quantitative multivariate central limit theorems for general functionals of possibly non-symmetric and non-homogeneous infinite Rademacher sequences are proved by combining discrete Malliavin calculus with the smart path method for normal approximation. In particular, a discrete multivariate second-order Poincar\'e inequality is developed. As a first application, the normal approximation of vectors of subgraph counting statistics in the Erd\H{o}s-R\'enyi random graph is considered. In this context, we further specialize to the normal approximation of vectors of vertex degrees. In a second application we prove a quantitative multivariate central limit theorem for vectors of intrinsic volumes induced by random cubical complexes.
Cite
@article{arxiv.1701.07365,
title = {Multivariate central limit theorems for Rademacher functionals with applications},
author = {Kai Krokowski and Christoph Thaele},
journal= {arXiv preprint arXiv:1701.07365},
year = {2017}
}