Cutoff ergodicity bounds in Wasserstein distance for a viscous energy shell model with Lévy noise
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909388329975808 |
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| author | Barrera, Gerardo Högele, Michael A. Pardo, Juan Carlos Pavlyukevich, Ilya |
| author_facet | Barrera, Gerardo Högele, Michael A. Pardo, Juan Carlos Pavlyukevich, Ilya |
| contents | 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 $α$-stable Lévy process, a stationary Gaussian or $α$-stable Ornstein-Uhlenbeck process, or by a general Lévy 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_13968 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cutoff ergodicity bounds in Wasserstein distance for a viscous energy shell model with Lévy noise Barrera, Gerardo Högele, Michael A. Pardo, Juan Carlos Pavlyukevich, Ilya Mathematical Physics Dynamical Systems Probability 60H10, 37L15, 37L60, 76M35, 76F20 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 $α$-stable Lévy process, a stationary Gaussian or $α$-stable Ornstein-Uhlenbeck process, or by a general Lévy 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. |
| title | Cutoff ergodicity bounds in Wasserstein distance for a viscous energy shell model with Lévy noise |
| topic | Mathematical Physics Dynamical Systems Probability 60H10, 37L15, 37L60, 76M35, 76F20 |
| url | https://arxiv.org/abs/2302.13968 |