Lengths of closed geodesics on random surfaces of large genus

  • Maryam Mirzakhani

  • Bram Petri

    Sorbonne Université, Paris, France
Lengths of closed geodesics on random surfaces of large genus cover

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Abstract

We prove Poisson approximation results for the bottom part of the length spectrum of a random closed hyperbolic surface of large genus. Here, a random hyperbolic surface is a surface picked at random using the Weil–Petersson volume form on the corresponding moduli space. As an application of our result, we compute the large genus limit of the expected systole.

Cite this article

Maryam Mirzakhani, Bram Petri, Lengths of closed geodesics on random surfaces of large genus. Comment. Math. Helv. 94 (2019), no. 4, pp. 869–889

DOI 10.4171/CMH/477