A simplified second-order Gaussian Poincaré inequality in discrete setting with applications
A simplified second-order Gaussian Poincaré inequality in discrete setting with applications
复制标题
离散环境下简化的二阶高斯庞加莱不等式及其应用
DOI：
10.1214/22-aihp1247
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Guangqu Zheng
中科院分区：
文献类型：
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作者：
P. Eichelsbacher;Benedikt Rednoss;Christoph Thale;Guangqu Zheng
.本文导出了无穷多Rademacher随机变量泛函正态逼近的一个简化的艾德二阶Gaussian Poincaré不等式.它是基于一个新的边界之间的Kolmogorov距离的一般Rademacher功能和高斯随机变量，这是建立通过离散Malliavin-Stein方法，是独立的兴趣。作为应用，讨论了Erdens-Rényi随机图中具有规定度的顶点数和子图计数统计量.固定度的顶点的数量也研究了渗透的汉明超立方体。此外，在Linial-Meshulam-Wallach随机κ-复形和无限加权2-游程中的孤立面的数目被处理。
. 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.