Discrete Malliavin-Stein method: Berry-Esseen bounds for random graphs and percolation
Probability
2015-11-13 v2 Combinatorics
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 Erd\H{o}s-Renyi random graph. A further application deals with a percolation problem on trees.
Keywords
Cite
@article{arxiv.1503.01029,
title = {Discrete Malliavin-Stein method: Berry-Esseen bounds for random graphs and percolation},
author = {Kai Krokowski and Anselm Reichenbachs and Christoph Thaele},
journal= {arXiv preprint arXiv:1503.01029},
year = {2015}
}