Ergodicity bounds for stable Ornstein-Uhlenbeck systems in Wasserstein distance with applications to cutoff stability. (English) Zbl 1541.60061
Summary: 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.
©2023 American Institute of Physics
©2023 American Institute of Physics
MSC:
| 60J65 | Brownian motion |
| 60G51 | Processes with independent increments; Lévy processes |
| 60G50 | Sums of independent random variables; random walks |
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