{"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":56114,"journal":{"name":"Journal of Topology","volume":"16 1","pages":"106-175"},"PeriodicalIF":0.8000,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12276","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","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:
期刊介绍：
The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal.
The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.
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