Trends to equilibrium for a class of relativistic diffusions

TL;DR

This paper investigates the convergence to equilibrium for a broad class of relativistic diffusions, establishing exponential decay rates using spectral gap analysis and Lyapunov methods.

Contribution

It generalizes previous results by proving exponential convergence for a large class of relativistic diffusions using spectral gap and Lyapunov techniques.

Findings

Existence of a spectral gap for the class C of relativistic diffusions.

Exponential decay of the distance to equilibrium in L2-norm.

Exponential decay of the distance to equilibrium in total variation.

Abstract

We address the question of the trends to equilibrium for a large class C of relativistic diffusions. We show the existence of a spectral gap using the Lyapounov method and deduce the exponential decay of the distance to equilibrium in L2-norm and in total variation. A similar result was obtained recently in arXiv:1009.5086 for a particular process of the class C.