Discrete Malliavin-Stein method: Berry-Esseen bounds for random graphs and percolation

Abstract

A new Berry-Esseen bound for non-linear functionals of non-symmetric and non-homogeneous infinite Rademacher sequences is established. It is based on a discrete version of the Malliavin-Stein method and an analysis of the discrete Ornstein-Uhlenbeck semigroup. The result is applied to sub-graph counts and to the number of vertices having a prescribed degree in the Erdős-Renyi random graph. A further application deals with a percolation problem on trees.

References in corpus (1)

• Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences

Cited by in corpus (4)

• Fourth moment theorems on the Poisson space in any dimension
• Normal approximation and almost sure central limit theorem for non-symmetric Rademacher functionals
• Poisson approximation of Rademacher functionals by the Chen-Stein method and Malliavin calculus
• Multivariate central limit theorems for Rademacher functionals with applications