{"title":"圆正交多项式集合的中观普遍性","authors":"Jonathan Breuer, Daniel Ofner","doi":"arxiv-2409.09803","DOIUrl":null,"url":null,"abstract":"We study mesoscopic fluctuations of orthogonal polynomial ensembles on the\nunit circle. We show that asymptotics of such fluctuations are stable under\ndecaying perturbations of the recurrence coefficients, where the appropriate\ndecay rate depends on the scale considered. By directly proving Gaussian limits\nfor certain constant coefficient ensembles, we obtain mesoscopic scale Gaussian\nlimits for a large class of orthogonal polynomial ensembles on the unit circle. As a corollary we prove mesocopic central limit theorems (for all mesoscopic\nscales) for the $\\beta=2$ circular Jacobi ensembles with real parameter\n$\\delta>-1/2$.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"30 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mesoscopic Universality for Circular Orthogonal Polynomial Ensembles\",\"authors\":\"Jonathan Breuer, Daniel Ofner\",\"doi\":\"arxiv-2409.09803\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study mesoscopic fluctuations of orthogonal polynomial ensembles on the\\nunit circle. We show that asymptotics of such fluctuations are stable under\\ndecaying perturbations of the recurrence coefficients, where the appropriate\\ndecay rate depends on the scale considered. By directly proving Gaussian limits\\nfor certain constant coefficient ensembles, we obtain mesoscopic scale Gaussian\\nlimits for a large class of orthogonal polynomial ensembles on the unit circle. As a corollary we prove mesocopic central limit theorems (for all mesoscopic\\nscales) for the $\\\\beta=2$ circular Jacobi ensembles with real parameter\\n$\\\\delta>-1/2$.\",\"PeriodicalId\":501245,\"journal\":{\"name\":\"arXiv - MATH - Probability\",\"volume\":\"30 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09803\",\"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 - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09803","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Mesoscopic Universality for Circular Orthogonal Polynomial Ensembles
We study mesoscopic fluctuations of orthogonal polynomial ensembles on the
unit circle. We show that asymptotics of such fluctuations are stable under
decaying perturbations of the recurrence coefficients, where the appropriate
decay rate depends on the scale considered. By directly proving Gaussian limits
for certain constant coefficient ensembles, we obtain mesoscopic scale Gaussian
limits for a large class of orthogonal polynomial ensembles on the unit circle. As a corollary we prove mesocopic central limit theorems (for all mesoscopic
scales) for the $\beta=2$ circular Jacobi ensembles with real parameter
$\delta>-1/2$.