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. 869–889DOI 10.4171/CMH/477