{"title":"Wigner空间上的自由定量四矩定理","authors":"S. Bourguin, Simon Campese","doi":"10.1093/IMRN/RNX036","DOIUrl":null,"url":null,"abstract":"We prove a quantitative Fourth Moment Theorem for Wigner integrals of any order with symmetric kernels, generalizing an earlier result from Kemp et al. (2012). The proof relies on free stochastic analysis and uses a new biproduct formula for bi-integrals. A consequence of our main result is a Nualart-Ortiz-Latorre type characterization of convergence in law to the semicircular distribution for Wigner integrals. As an application, we provide Berry-Esseen type bounds in the context of the free Breuer-Major theorem for the free fractional Brownian motion.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Free quantitative fourth moment theorems on Wigner space\",\"authors\":\"S. Bourguin, Simon Campese\",\"doi\":\"10.1093/IMRN/RNX036\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a quantitative Fourth Moment Theorem for Wigner integrals of any order with symmetric kernels, generalizing an earlier result from Kemp et al. (2012). The proof relies on free stochastic analysis and uses a new biproduct formula for bi-integrals. A consequence of our main result is a Nualart-Ortiz-Latorre type characterization of convergence in law to the semicircular distribution for Wigner integrals. As an application, we provide Berry-Esseen type bounds in the context of the free Breuer-Major theorem for the free fractional Brownian motion.\",\"PeriodicalId\":351745,\"journal\":{\"name\":\"arXiv: Operator Algebras\",\"volume\":\"6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-01-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Operator Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/IMRN/RNX036\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/IMRN/RNX036","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
摘要
我们证明了具有对称核的任意阶Wigner积分的定量第四矩定理，推广了Kemp et al.(2012)的早期结果。该证明依赖于自由随机分析，并使用了双积分的一个新的双积公式。我们的主要结果的一个结果是对Wigner积分的半圆分布收敛规律的nualart - ortize - latorre型表征。作为一个应用，我们给出了自由分数阶布朗运动的自由Breuer-Major定理背景下的Berry-Esseen型界。
Free quantitative fourth moment theorems on Wigner space
We prove a quantitative Fourth Moment Theorem for Wigner integrals of any order with symmetric kernels, generalizing an earlier result from Kemp et al. (2012). The proof relies on free stochastic analysis and uses a new biproduct formula for bi-integrals. A consequence of our main result is a Nualart-Ortiz-Latorre type characterization of convergence in law to the semicircular distribution for Wigner integrals. As an application, we provide Berry-Esseen type bounds in the context of the free Breuer-Major theorem for the free fractional Brownian motion.
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