Experiments suggesting that the distribution of the hyperbolic length of closed geodesics sampling by word length is Gaussian

2013/05/25 by Chas, Moira, Li, Keren, Maskit, Bernard · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT) #Primary 57M50 #secondary 37E35

paper · doi:10.48550/arxiv.1305.5912

Abstract

Each free homotopy class of directed closed curves on a surface with boundary can be described by a cyclic reduced word in the generators of the fundamental group and their inverses. The word length is the number of letters of the cyclic word. If the surface has a hyperbolic metric with geodesic boundary, the geometric length of the class is the length of the unique geodesic. By computer experiments, we investigate the distribution of the geometric length among all classes with a given word length in the pair of pants surface. Our experiments strongly suggest that the distribution is normal.

Cited by

• Normal distribution of Lyapunov exponents of periodic orbits for expanding circle maps

Related

• The length of closed geodesics on random Riemann Surfaces
• Counting Mapping Class group orbits on hyperbolic surfaces
• Word length statistics for Teichm "uller geodesics and singularity of\n harmonic measure
• Probability laws for the distribution of geometric lengths when sampling\n by a random walk in a Fuchsian fundamental group
• Distribution in the unit tangent bundle of the geodesics of given type