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

• Kai Krokowski ^[1] ; Anselm Reichenbachs ^[1] ; Christoph Thäle ^[1]
  1. [1] Ruhr University Bochum

     Ruhr University Bochum

     Kreisfreie Stadt Bochum, Alemania

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 2, 2017, págs. 1071-1109
• Idioma: inglés
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• Resumen

  • 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.