Weil-Petersson体积的增长性与大亏格的随机双曲曲面
Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus
摘要：
本文研究了亏格为$g$的双曲曲面模空间的Weil-Petersson体积的渐近性质，并将这些渐近估计用于研究随机双曲曲面的几何性质，如Cheeger常数和给定组合类型的最短单闭测地线的长度.
英文摘要：
In this paper we study the asymptotic behavior of Weil-Petersson volumes of moduli spaces of hyperbolic surfaces of genus $g$ as $g \rightarrow \infty.$ We apply these asymptotic estimates to study the geometric properties of random hyperbolic surfaces, such as the Cheeger constant and the length of the shortest simple closed geodesic of a given combinatorial type.
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