Corpus ID: 236976344

A simplified second-order Gaussian Poincar\'e inequality in discrete setting with applications

  title={A simplified second-order Gaussian Poincar\'e inequality in discrete setting with applications},
  author={Peter Eichelsbacher and Benedikt Rednoss and Christoph Thale and Guangqu Zheng},
Abstract. In this paper, a simplified second-order Gaussian Poincaré inequality for normal approximation of functionals over infinitely many Rademacher random variables is derived. It is based on a new bound for the Kolmogorov distance between a general Rademacher functional and a Gaussian random variable, which is established by means of the discrete Malliavin-Stein method and is of independent interest. As an application, the number of vertices with prescribed degree and the subgraph counting… Expand

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