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March 2017 Discrete Malliavin–Stein method: Berry–Esseen bounds for random graphs and percolation
Kai Krokowski, Anselm Reichenbachs, Christoph Thäle
Ann. Probab. 45(2): 1071-1109 (March 2017). DOI: 10.1214/15-AOP1081

Abstract

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 sub-graph counts and to the number of vertices having a prescribed degree in the Erdős–Rényi random graph. A further application deals with a percolation problem on trees.

Citation

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Kai Krokowski. Anselm Reichenbachs. Christoph Thäle. "Discrete Malliavin–Stein method: Berry–Esseen bounds for random graphs and percolation." Ann. Probab. 45 (2) 1071 - 1109, March 2017. https://doi.org/10.1214/15-AOP1081

Information

Received: 1 March 2015; Revised: 1 November 2015; Published: March 2017
First available in Project Euclid: 31 March 2017

zbMATH: 1372.05203
MathSciNet: MR3630293
Digital Object Identifier: 10.1214/15-AOP1081

Subjects:
Primary: 05C80, 60F05, 60H07, 82B43

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 2 • March 2017
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