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Growth of weil-petersson volumes and random hyperbolic surfaces of large genus

Maryam Mirzakhani Stanford University

Differential Geometry mathscidoc:1609.10315

Journal of Differential Geometry, 94, (2), 267-300, 2013
In this paper, we investigate the geometric properties of random hyperbolic surfaces of large genus. We describe the relationship between the behavior of lengths of simple closed geodesics on a hyperbolic surface and properties of the moduli space of such surfaces. First, we study the asymptotic behavior of Weil-Petersson volume Vg,n of the moduli spaces of hyperbolic surfaces of genus g with n punctures as g → ∞. Then we discuss basic geometric properties of a random hyperbolic surface of genus g with respect to the Weil-Petersson measure as g → ∞.
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@inproceedings{maryam2013growth,
  title={GROWTH OF WEIL-PETERSSON VOLUMES AND RANDOM HYPERBOLIC SURFACES OF LARGE GENUS},
  author={Maryam Mirzakhani},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914075755690198977},
  booktitle={Journal of Differential Geometry},
  volume={94},
  number={2},
  pages={267-300},
  year={2013},
}
Maryam Mirzakhani. GROWTH OF WEIL-PETERSSON VOLUMES AND RANDOM HYPERBOLIC SURFACES OF LARGE GENUS. 2013. Vol. 94. In Journal of Differential Geometry. pp.267-300. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914075755690198977.
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