New lower bound on ball packing density in high-dimensional hyperbolic spaces

TL;DR

This paper establishes a new lower bound on the maximum density of ball packings in high-dimensional hyperbolic spaces, surpassing previous bounds by leveraging recent graph theory results.

Contribution

It introduces an improved lower bound on hyperbolic ball packing density using advanced graph theoretical methods, extending prior bounds significantly.

Findings

New lower bound improves previous estimates

Bound scales with dimension m and radius R

Utilizes recent graph theory theorems

Abstract

We present a new lower bound on the Bowen-Radin maximal density of radius-R ball packings in the m-dimensional hyperbolic space, improving on the basic covering bound by factor \Omega(m(R+\ln m)) as m tends to infinity. This is done by applying the recent theorem of Campos, Jenssen, Michelen and Sahasrabudhe on independent sets in graphs with sparse neighbourhoods.