{"title":"Central limit theorem for CβE pair dependent statistics in mesoscopic regime","authors":"A. Aguirre, A. Soshnikov","doi":"10.1214/22-ecp481","DOIUrl":null,"url":null,"abstract":"We extend our results on the fluctuation of the pair counting statistic of the Circular Beta Ensemble (cid:80) i (cid:54) = j f ( L N ( θ i − θ j )) for arbitrary β > 0 in the mesoscopic regime L N = O ( N 2 / 3 − (cid:15) ) . In addition, we obtain similar results for bipartite statistics.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Communications in Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/22-ecp481","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
We extend our results on the fluctuation of the pair counting statistic of the Circular Beta Ensemble (cid:80) i (cid:54) = j f ( L N ( θ i − θ j )) for arbitrary β > 0 in the mesoscopic regime L N = O ( N 2 / 3 − (cid:15) ) . In addition, we obtain similar results for bipartite statistics.
期刊介绍：
The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.
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