The Annals of Probability
- Ann. Probab.
- Volume 45, Number 2 (2017), 1071-1109.
Discrete Malliavin–Stein method: Berry–Esseen bounds for random graphs and percolation
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.
Ann. Probab., Volume 45, Number 2 (2017), 1071-1109.
Received: March 2015
Revised: November 2015
First available in Project Euclid: 31 March 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 05C80: Random graphs [See also 60B20] 60F05: Central limit and other weak theorems 60H07: Stochastic calculus of variations and the Malliavin calculus 82B43: Percolation [See also 60K35]
Krokowski, Kai; Reichenbachs, Anselm; Thäle, Christoph. Discrete Malliavin–Stein method: Berry–Esseen bounds for random graphs and percolation. Ann. Probab. 45 (2017), no. 2, 1071--1109. doi:10.1214/15-AOP1081. https://projecteuclid.org/euclid.aop/1490947314