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:

中文翻译：

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随机曲面上分离封闭测地线长度的大亏格渐近

在本文中，我们研究了亏格随机双曲曲面的基本几何量$G$关于模空间上的 Weil-Petersson 测度${\mathcal{米}}_G$. 我们表明作为$G$走向无穷大，一个通用的表面$X\in {\mathcal{米}}_G$渐近地满足：