{"title":"Large genus asymptotics for lengths of separating closed geodesics on random surfaces","authors":"Xin Nie, Yunhui Wu, Yuhao Xue","doi":"10.1112/topo.12276","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we investigate basic geometric quantities of a random hyperbolic surface of genus <math>\n <semantics>\n <mi>g</mi>\n <annotation>$g$</annotation>\n </semantics></math> with respect to the Weil–Petersson measure on the moduli space <math>\n <semantics>\n <msub>\n <mi>M</mi>\n <mi>g</mi>\n </msub>\n <annotation>$\\mathcal {M}_g$</annotation>\n </semantics></math>. We show that as <math>\n <semantics>\n <mi>g</mi>\n <annotation>$g$</annotation>\n </semantics></math> goes to infinity, a generic surface <math>\n <semantics>\n <mrow>\n <mi>X</mi>\n <mo>∈</mo>\n <msub>\n <mi>M</mi>\n <mi>g</mi>\n </msub>\n </mrow>\n <annotation>$X\\in \\mathcal {M}_g$</annotation>\n </semantics></math> satisfies asymptotically: \n\n </p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12276","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 18
Abstract
In this paper, we investigate basic geometric quantities of a random hyperbolic surface of genus with respect to the Weil–Petersson measure on the moduli space . We show that as goes to infinity, a generic surface satisfies asymptotically:
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