Cutoff Thermalization for Ornstein–Uhlenbeck Systems with Small Lévy Noise in the Wasserstein Distance

• Published in: Journal of statistical physics Vol. 184; no. 3
• Main Authors: Barrera, G., Högele, M. A., Pardo, J. C.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2021; Springer; Springer Nature B.V
• Subjects: Brownian motion; Eigenvectors; Low temperature; Mathematical and Computational Physics; Noise; Orthogonality; Oscillators; Physical Chemistry; Physics; Physics and Astronomy; Quantum Physics; Statistical Physics and Dynamical Systems; Theoretical; Thermalization (energy absorption); Time dependence; Windows (intervals); Nonnormal growth; Wasserstein distance; The cutoff phenomenon; Ornstein–Uhlenbeck processes; Abrupt convergence; Shift linearity of the Wasserstein distance

This article establishes cutoff thermalization (also known as the cutoff phenomenon ) for a class of generalized Ornstein–Uhlenbeck systems ( X t ε ( x ) ) t ⩾ 0 with ε -small additive Lévy noise and initial value x . The driving noise processes include Brownian motion, α -stable Lévy flights, finit...