Ergodicity bounds for stable Ornstein-Uhlenbeck systems in Wasserstein distance with applications to cutoff stability

Gerardo Barrera; Michael A Högele

doi:10.1063/5.0164204

Ergodicity bounds for stable Ornstein-Uhlenbeck systems in Wasserstein distance with applications to cutoff stability

Chaos. 2023 Nov 1;33(11):113124. doi: 10.1063/5.0164204.

Authors

Gerardo Barrera¹, Michael A Högele²

Affiliations

¹ Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, Pietari Kalmin katu 5, FI-00014 Helsinki, Finland.
² Departamento de Matemáticas, Universidad de los Andes, Facultad de Ciencias, Cra 1 # 18A - 12, 111711 Bogotá, Colombia.

PMID: 37975874
DOI: 10.1063/5.0164204

Abstract

This article establishes cutoff stability also known as abrupt thermalization for generic multidimensional Hurwitz stable Ornstein-Uhlenbeck systems with (possibly degenerate) Lévy noise at fixed noise intensity. The results are based on several ergodicity quantitative lower and upper bounds some of which make use of the recently established shift linearity property of the Wasserstein-Kantorovich-Rubinstein distance by the authors. It covers such irregular systems like Jacobi chains and more general networks of coupled harmonic oscillators with a heat bath (including Lévy excitations) at constant temperature on the outer edges and the so-called Brownian gyrator.