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.
"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