The speed of relaxation for diffusion with drift satisfying exponential decay of correlations
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- by Brice Franke and Thi-Hien Nguyen PDF
- Proc. Amer. Math. Soc. 146 (2018), 2425-2434 Request permission
Abstract:
We study the convergence speed in the $L^2$-norm of the diffusion semigroup toward its equilibrium when the underlying flow satisfies decay of correlation. Our result is an extension of the main theorem given by Constantin, Kiselev, Ryzhik and Zlatoš (2008). Our proof is based on Weyl asymptotic law for the eigenvalues of the Laplace operator, Sobolev imbedding and some assumption on decay of correlation for the underlying flow.References
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Additional Information
- Brice Franke
- Affiliation: Laboratiore de Mathématiques de Bretagne Atlantique UMR 6205, UFR Sciences et Techniques, Université de Bretagne Occidentale, 6 Avenue Le Gorgeu, CS 93837, 29238 Brest, cedex 3, France
- MR Author ID: 728183
- Email: brice.franke@univ-brest.fr
- Thi-Hien Nguyen
- Affiliation: Laboratiore de Mathématiques de Bretagne Atlantique UMR 6205, UFR Sciences et Techniques, Université de Bretagne Occidentale, 6 Avenue Le Gorgeu, CS 93837, 29238 Brest, cedex 3, France
- Email: thi-hien.nguyen@univ-brest.fr
- Received by editor(s): May 22, 2015
- Received by editor(s) in revised form: April 27, 2016
- Published electronically: February 28, 2018
- Additional Notes: The authors would like to thank their colleague Benoît Saussol for directing their attention to the notion of decay of correlation and Sheu Shuenn-Jyi for some helpful comments during a talk at National Central Taiwan University.
- Communicated by: Joachim Krieger
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2425-2434
- MSC (2010): Primary 35K10; Secondary 37A25, 60J60
- DOI: https://doi.org/10.1090/proc/13268
- MathSciNet review: 3778146