Lengths of closed geodesics on random surfaces of large genus
Geometric Topology
2021-03-18 v2 Probability
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.
Keywords
Cite
@article{arxiv.1710.09727,
title = {Lengths of closed geodesics on random surfaces of large genus},
author = {Maryam Mirzakhani and Bram Petri},
journal= {arXiv preprint arXiv:1710.09727},
year = {2021}
}
Comments
21 pages, final version