# 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}
}
• M. Mirzakhani
• Published 10 December 2010
• Mathematics
• arXiv: General Topology
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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