Multivariate central limit theorems for Rademacher functionals with applications

作者：Krokowski Kai^*; Thaele Christoph

来源：Electronic Journal of Probability, 2017, 22(0): 87.

DOI：10.1214/17-EJP106

• discrete Malliavin calculus
• intrinsic volume
• multivariate central limit theorem
• smart path method
• subgraph count
• random graph
• random cubical complex
• vertex degree

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 Poincare inequality is developed. As a first application, the normal approximation of vectors of subgraph counting statistics in the Erdos-Renyi 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.

• 出版日期2017