Commentarii Mathematici Helvetici
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Published online: 2019-12-18
Lengths of closed geodesics on random surfaces of large genusMaryam Mirzakhani and Bram Petri (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