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

Authors
Krokowski, Kai Reichenbachs, Anselm Thäle, Christoph
Citation
Krokowski, Kai et al., Discrete Malliavin.Stein method: Berry.Esseen bounds for random graphs and percolation, Annals of probability (Online) , 45(2), 2017, pp. 1071-1109
Journal title
Annals of probability (Online) → ACNP
ISSN journal
2168894X
Volume
45
Issue
2
Year of publication
2017
Pages
1071 - 1109
Database
ACNP
SICI code
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 Erd.s.Rényi random graph. A further application deals with a percolation problem on trees.