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Commentarii Mathematici Helvetici

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Volume 94, Issue 4, 2019, pp. 869–889
DOI: 10.4171/CMH/477

Published online: 2019-12-18

Lengths of closed geodesics on random surfaces of large genus

Maryam Mirzakhani and Bram Petri[1]

(1) Sorbonne Université, Paris, France

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.

Keywords: Random hyperbolic surfaces, Weil–Petersson volumes

Mirzakhani Maryam, Petri Bram: Lengths of closed geodesics on random surfaces of large genus. Comment. Math. Helv. 94 (2019), 869-889. doi: 10.4171/CMH/477