Krokowski, Kai et al., Discrete Malliavin.Stein method: Berry.Esseen bounds for random graphs and percolation, Annals of probability , 45(2), 2017, pp. 1071-1109
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.