# Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus

@article{Mirzakhani2010GrowthOW, title={Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus}, author={Maryam Mirzakhani}, journal={arXiv: General Topology}, year={2010} }

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.

## 85 Citations

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We explicitly compute the diverging factor in the large genus asymptotics of the Weil–Petersson volumes of the moduli spaces of n-pointed complex algebraic curves. Modulo a universal multiplicative…

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