Large genus asymptotics for lengths of separating closed geodesics on random surfaces

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2023-01-09 DOI:10.1112/topo.12276

Xin Nie, Yunhui Wu, Yuhao Xue

引用次数: 18

Abstract

In this paper, we investigate basic geometric quantities of a random hyperbolic surface of genus $g$ with respect to the Weil–Petersson measure on the moduli space $M_{g}$ . We show that as $g$ goes to infinity, a generic surface $X \in M_{g}$ satisfies asymptotically:

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随机曲面上分离闭测地线长度的大亏格渐近性

在本文中，我们研究了关于模空间Mg$\mathcal上的Weil–Petersson测度的g$g$亏格随机双曲面的基本几何量{M}_g$。我们证明了当g$g$到无穷大时，一般曲面X∈Mg$X\in\mathcal{M}_g$渐近满足：（1）X$X$的分离收缩期约为2logg$2\log g\hbox｛\it；｝$（2）在X上的任何分离收缩曲线周围都有一个宽度约为logg2$\frac｛\log g｝｛2｝$的半轴环$X\hbox｛\it；｝$（3）X$X$上最短分离闭合多测地线的长度约为2logg$2\logg$。作为应用，我们还讨论了极值分离收缩期、非简单收缩期的渐近行为，以及当g$g$变为无穷大时最短分离闭合多测地线的预期长度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

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.