The speed of relaxation for diffusion with drift satisfying exponential decay of correlations

Franke, Brice; Nguyen, Thi-Hien

doi:10.1090/proc/13268

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.

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