A simplified second-order Gaussian Poincaré inequality in discrete setting with applications

IF 1.5 Q2 PHYSICS, MATHEMATICAL Annales de l Institut Henri Poincare D Pub Date : 2021-08-11 DOI:10.1214/22-AIHP1247
P. Eichelsbacher, Benedikt Rednoss, Christoph Thale, Guangqu Zheng
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引用次数: 2

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 statistic in the Erdős-Rényi 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 κ -complex and infinite weighted 2-runs are treated.
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离散情况下二阶高斯庞卡罗不等式的简化及其应用
。本文导出了无穷多个Rademacher随机变量上泛函正态逼近的一个简化二阶高斯poincar不等式。它基于一般Rademacher泛函与高斯随机变量之间的Kolmogorov距离的新界,该界是用离散Malliavin-Stein方法建立的,具有独立的意义。作为应用,讨论了Erdős-Rényi随机图中具有规定度数的顶点数和子图计数统计量。研究了汉明超立方体上的渗滤液的定度顶点数。此外,对Linial-Meshulam-Wallach随机κ -复合体和无限加权2-run中的孤立面数量进行了处理。
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CiteScore
2.30
自引率
0.00%
发文量
16
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