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arXiv · 1503.01029

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

Kai Krokowski·Anselm Reichenbachs·Christoph Thaele
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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.

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Kai Krokowski, Anselm Reichenbachs, Christoph Thaele. 2015-03-03. Discrete Malliavin-Stein method: Berry-Esseen bounds for random graphs and percolation. https://arxiv.org/abs/1503.01029

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