论文标题
大属渐近属，用于在随机表面上分离闭合的大地学的长度
Large genus asymptotics for lengths of separating closed geodesics on random surfaces
论文作者
论文摘要
在本文中，我们研究了属$ g $的随机双曲表面的基本几何量，相对于模量空间$ \ mathcal {m} _g $的Weil-Petersson测量。我们表明，随着$ g $进入无限，\ Mathcal {m} _g $ in Infinity y Infinity a in Infinity：（1）$ x $的分离收缩期约为$ 2 \ log g $; （2）宽度约为$ \ frac {\ log g} {2} $，围绕$ x $的分离收缩曲线; （3）$ x $的最短封闭的多晶格的最短长度约为$ 2 \ log g $。作为应用程序，我们还讨论了极端分离收缩期，非简单收缩期的渐近行为以及最短分离封闭的多晶格的期望值，因为$ g $将用于无限。
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 $\mathcal{M}_g$. We show that as $g$ goes to infinity, a generic surface $X\in \mathcal{M}_g$ satisfies asymptotically: (1) the separating systole of $X$ is about $2\log g$; (2) there is a half-collar of width about $\frac{\log g}{2}$ around a separating systolic curve of $X$; (3) the length of shortest separating closed multi-geodesics of $X$ is about $2\log g$. As applications, we also discuss the asymptotic behavior of the extremal separating systole, the non-simple systole and the expectation value of lengths of shortest separating closed multi-geodesics as $g$ goes to infinity.
