Work

Lengths of saddle connections on random translation surfaces of large genus

Year: 2026

Type: article

Abstract: We determine the distribution of the number of saddle connections on a random translation surface of large genus. More specifically, for genus g tending to infinity, the number of saddle connections with lengths in a given interval [a/g, b/g] converges in distribution to a Poisson distributed random variable. Furthermore, the numbers of saddle connections associated to disjoint intervals of lengths are independent.

Source: Commentarii Mathematici Helvetici

DOI: 10.4171/cmh/623

Authors: Howard Masur, Kasra Rafi, Anja Randecker

Institutions: University of Chicago, University of Toronto, Heidelberg University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4405354399

FWCI: 11.39

Cites:

Cited by: 1

Related to: 10