Experimental statistics for Mirzakhani's Theorem

TL;DR

This paper provides experimental evidence supporting Mirzakhani's theorem by demonstrating that on a genus two surface, separating and non-separating curves occur in a 1:48 ratio, confirming theoretical predictions.

Contribution

It offers the first experimental verification of Mirzakhani's ratio for specific curve types on genus two surfaces.

Findings

Separation and non-separation curves occur in a 1:48 ratio.

Experimental data supports Mirzakhani's theoretical result.

Methodology for obtaining statistical evidence is described.

Abstract

In her seminal 2008 paper, Maryam Mirzakhani showed that the ratio that two topological types of curves occur in is a rational number. In this paper we describe the process by which we obtained experimental evidence that separating and non-separating curves on the surface of genus two occur in the ratio 1 : 48.