DISCRETE MALLIAVIN-STEIN METHOD: BERRY-ESSEEN BOUNDS FOR RANDOM GRAPHS AND PERCOLATION

• 成果类型: Article
• 署名作者: Krokowski, Kai; Reichenbachs, Anselm; Thaele, Christoph
• 署名单位: Ruhr University Bochum
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1081
• 发表日期: 2017
• 页码: 1071-1109
• 关键词: CENTRAL LIMIT-THEOREMS; U-statistics; gaussian fluctuations; stochastic-analysis; Poisson; approximation; moments

摘要

A new Berry-Esseen bound for nonlinear functionals of nonsymmetric and nonhomogeneous 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 subgraph counts and to the number of vertices having a prescribed degree in the Erd os-Renyi random graph. A further application deals with a percolation problem on trees.