Lengths of closed geodesics on random surfaces of large genus
By Maryam Mirzakhani, Bram Petri. 2017
79 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4ae7e4be1b151c43142f10d5897dc2137d67f5e5
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A tour through Mirzakhani’s work on moduli spaces of Riemann surfaces (2019, methodology): “ able to study H(X) using the techniques in the example. The result on 1 follows from the Cheeger inequality 1 h(X)2=4. We conclude with a special case of the main result of Mirzakhani and Petri [MP17]. Theorem 10.2. For any 0 <a<b, the number of primitive closed geodesics of length in [a;b]”