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

This article establishes cutoff stability also known as abrupt thermalization for generic multidimensional Hurwitz stable Ornstein-Uhlenbeck systems with (possibly degenerate) L\'evy 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 L\'evy excitations) at constant temperature on the outer edges and the so-called Brownian gyrator.Comment: 29 pages, 3 figure

Moment estimates in the first Borel-Cantelli Lemma with applications to mean deviation frequencies

We quantify the elementary Borel-Cantelli Lemma by higher moments of the overlap count statistic in terms of the weighted summability of the probabilities. Applications include mean deviation frequencies in the Strong Law and the Law of the Iterated Logarithm

Cutoff Thermalization for Ornstein-Uhlenbeck Systems with Small Levy Noise in the Wasserstein Distance : Cutoff Thermalization for Ornstein–Uhlenbeck Systems...

This article establishes cutoff thermalization (also known as the cutoff phenomenon) for a class of generalized Ornstein-Uhlenbeck systems with small additive Lévy noise and any nonzero initial value.Peer reviewe