A central limit theorem for random closed geodesics: proof of the Chas-Li-Maskit conjecture

TL;DR

This paper establishes a central limit theorem for the lengths of closed geodesics on hyperbolic surfaces, confirming a conjecture for the specific case of hyperbolic pairs of pants.

Contribution

It proves a general central limit theorem for closed geodesic lengths and resolves the Chas-Li-Maskit conjecture for hyperbolic pairs of pants.

Findings

Central limit theorem applies to geodesic lengths on hyperbolic surfaces.

Confirmed the Chas-Li-Maskit conjecture for hyperbolic pairs of pants.

Provides a probabilistic understanding of geodesic length distributions.

Abstract

We prove a central limit theorem for the length of closed geodesics in any compact orientable hyperbolic surface. In the special case of a hyperbolic pair of pants, this settles a conjecture of Chas-Li-Maskit.