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Journal Article

Lengths of closed geodesics on random surfaces of large genus

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Petri,  Bram
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.4171/CMH/477
(Publisher version)

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Citation

Mirzakhani, M., & Petri, B. (2019). Lengths of closed geodesics on random surfaces of large genus. Commentarii Mathematici Helvetici, 94(4), 869-889. doi:10.4171/CMH/477.


Cite as: https://hdl.handle.net/21.11116/0000-0006-40BC-E
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.