Quantitative multivariate central limit theorems for general functionals of independent, 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 Poincaré inequality is developed. As a first application, the normal approximation of vectors of subgraph counting statistics in the Erdős-Rényi 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.
"Multivariate central limit theorems for Rademacher functionals with applications." Electron. J. Probab. 22 1 - 30, 2017. https://doi.org/10.1214/17-EJP106