Lengths of closed geodesics on random surfaces of large genus

Maryam Mirzakhani; Bram Petri

doi:10.4171/cmh/477

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arXiv · 1710.09727

Lengths of closed geodesics on random surfaces of large genus

Maryam Mirzakhani·Bram Petri

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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.

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Maryam Mirzakhani, Bram Petri. 2017-10-26. Lengths of closed geodesics on random surfaces of large genus. https://doi.org/10.4171/cmh/477

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