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
{"title":"A simplified second-order Gaussian Poincaré inequality in discrete setting with applications","authors":"P. Eichelsbacher, Benedikt Rednoss, Christoph Thale, Guangqu Zheng","doi":"10.1214/22-AIHP1247","DOIUrl":null,"url":null,"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.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"5 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2021-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales de l Institut Henri Poincare D","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/22-AIHP1247","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
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.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
2.30
自引率
0.00%
发文量
16
期刊最新文献
A vertex model for supersymmetric LLT polynomials Duality of orthogonal and symplectic random tensor models Second order cumulants: Second order even elements and $R$-diagonal elements Fluctuations of dimer heights on contracting square-hexagon lattices Reflection of stochastic evolution equations in infinite dimensional domains
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1