A simplified second-order Gaussian Poincar\'e inequality in discrete setting with applications
Abstract
In this paper, a simplified second-order Gaussian Poincar\'e 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 statistic in the Erd\"os-R\'enyi random graph are discussed. The number of vertices of fixed degree is also studied for percolation on the Hamming hypercube. Moreover, the number of isolated faces in the Linial-Meshulam-Wallach random -complex and infinite weighted 2-runs are treated.
Cite
@article{arxiv.2108.05216,
title = {A simplified second-order Gaussian Poincar\'e inequality in discrete setting with applications},
author = {Peter Eichelsbacher and Benedikt Rednoß and Christoph Thäle and Guangqu Zheng},
journal= {arXiv preprint arXiv:2108.05216},
year = {2023}
}