Berry-Esseen bounds and multivariate limit theorems for functionals of   Rademacher sequences
  Berry-Esseen bounds for non-linear functionals of infinite Rademacher sequences are derived by means of the Malliavin-Stein method. Moreover, multivariate extensions for vectors of Rademacher functionals are shown. The results establish a connection to small-ball probabilities and shed new light onto the relation between central limit theorems on the Rademacher chaos and norms of contraction operators. Applications concern infinite weighted 2-runs, a combinatorial central limit theorem and traces of Bernoulli random matrices. 
Kai Krokowski, Anselm Reichenbachs and Christoph Thaele
math.PR