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Statistical Stability for Transport in Random Media

Thierry Goudon 1 Alexis F Vasseur 2 
1 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : We go back to the analysis of the transport of (classical or quantum) particles intime-dependent random media as proposed in [F. Poupaud and A. Vasseur,J. Math. Pures Appl.(9), 82 (2003), pp. 711–748], where the convergence of the expectation of solutions of the Liouvilleequation (resp., Wigner equation) to the solution of the Fokker-Planck equation (resp., Boltzmannequation) is established. Here we show that the convergence holds in probability. This result relieson certain scale separation properties of the scaling, as indicated by several counterexamples
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Submitted on : Wednesday, December 18, 2019 - 5:29:11 PM
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Thierry Goudon, Alexis F Vasseur. Statistical Stability for Transport in Random Media. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2019, 17 (1), pp.507-530. ⟨10.1137/18M1184643⟩. ⟨hal-02418394⟩



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