{"title":"Local central limit theorem for Mallows measure","authors":"Alexey Bufetov, Kailun Chen","doi":"arxiv-2409.10415","DOIUrl":null,"url":null,"abstract":"We study the statistics of the Mallows measure on permutations in the limit\npioneered by Starr (2009). Our main result is the local central limit theorem\nfor its height function. We also re-derive versions of the law of large numbers\nand the large deviation principle, obtain the standard central limit theorem\nfrom the local one, and establish a multi-point version of the local central\nlimit theorem.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","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-2409.10415","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study the statistics of the Mallows measure on permutations in the limit
pioneered by Starr (2009). Our main result is the local central limit theorem
for its height function. We also re-derive versions of the law of large numbers
and the large deviation principle, obtain the standard central limit theorem
from the local one, and establish a multi-point version of the local central
limit theorem.