A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone

Abstract

The Hilbert metric is a widely used tool for analysing the convergence of Markov processes and the ergodic properties of deterministic dynamical systems. A useful representation formula for the Hilbert metric was given by Liverani. The goal of the present paper is to extend this formula to the non-compact and multidimensional setting with a different cone, taylored for sub-Gaussian tails.

Keywords

• dynamical systems
• Hilbert metric
• Liverani’s formula