随机贝伊曲面的直径

arXiv: Geometric Topology Pub Date : 2019-10-25 DOI:10.2140/agt.2021.21.2929

Thomas Budzinski, N. Curien, Bram Petri

{"title":"随机贝伊曲面的直径","authors":"Thomas Budzinski, N. Curien, Bram Petri","doi":"10.2140/agt.2021.21.2929","DOIUrl":null,"url":null,"abstract":"We determine the asymptotic growth rate of the diameter of the random hyperbolic surfaces constructed by Brooks and Makover. This model consists of a uniform gluing of $2n$ hyperbolic ideal triangles along their sides followed by a compactification to get a random hyperbolic surface of genus roughly $n/2$. We show that the diameter of those random surfaces is asymptotic to $2 \\log n$ in probability as $n \\to \\infty$.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"21 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"The diameter of random Belyi surfaces\",\"authors\":\"Thomas Budzinski, N. Curien, Bram Petri\",\"doi\":\"10.2140/agt.2021.21.2929\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We determine the asymptotic growth rate of the diameter of the random hyperbolic surfaces constructed by Brooks and Makover. This model consists of a uniform gluing of $2n$ hyperbolic ideal triangles along their sides followed by a compactification to get a random hyperbolic surface of genus roughly $n/2$. We show that the diameter of those random surfaces is asymptotic to $2 \\\\log n$ in probability as $n \\\\to \\\\infty$.\",\"PeriodicalId\":8454,\"journal\":{\"name\":\"arXiv: Geometric Topology\",\"volume\":\"21 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-10-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/agt.2021.21.2929\",\"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: Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/agt.2021.21.2929","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 8

摘要

我们确定了Brooks和Makover构造的随机双曲曲面直径的渐近增长率。该模型由$2n$双曲理想三角形沿其侧面的均匀胶合组成，然后进行紧化以获得一个大致为$n/2$的随机双曲曲面。我们证明了这些随机曲面的直径在概率上是渐近于$2 \log n$的，如$n \to \infty$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The diameter of random Belyi surfaces

We determine the asymptotic growth rate of the diameter of the random hyperbolic surfaces constructed by Brooks and Makover. This model consists of a uniform gluing of $2n$ hyperbolic ideal triangles along their sides followed by a compactification to get a random hyperbolic surface of genus roughly $n/2$. We show that the diameter of those random surfaces is asymptotic to $2 \log n$ in probability as $n \to \infty$.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv: Geometric Topology

自引率

0.00%

发文量