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

Gerardo Barrera, Michael A. Högele

Published 2023-06-20Version 1

This article establishes cutoff stability or abrupt thermalization for generic multidimensional Hurwitz stable Ornstein-Uhlenbeck systems with moderate (possibly degenerate) L\'evy noise at constant noise intensity. The result is based on several ergodicity bounds which make use of the recently established shift linearity property of the Wasserstein distance by the authors. It covers such irregular systems like Jacobi chains of coupled harmonic oscillators with a heat bath at constant temperature on the outer edges.