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arXiv · 2302.13968

Cutoff ergodicity bounds in Wasserstein distance for a viscous energy shell model with L\'evy noise

Gerardo Barrera·Michael A. Högele·Juan Carlos Pardo·Ilya Pavlyukevich
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Abstract

This article establishes explicit non-asymptotic ergodic bounds in the renormalized Wasserstein-Kantorovich-Rubinstein (WKR) distance for a viscous energy shell lattice model of turbulence with random energy injection. The system under consideration is driven either by a Brownian motion, a symmetric $\alpha$-stable L\'evy process, a stationary Gaussian or $\alpha$-stable Ornstein-Uhlenbeck process, or by a general L\'evy process with second moments. The obtained non-asymptotic bounds establish asymptotically abrupt thermalization. The analysis is based on the explicit representation of the solution of the system in terms of convolutions of Bessel functions.

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Gerardo Barrera, Michael A. Högele, Juan Carlos Pardo, Ilya Pavlyukevich. 2023-02-27. Cutoff ergodicity bounds in Wasserstein distance for a viscous energy shell model with L\'evy noise. https://doi.org/10.1007/s10955-024-03308-6

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