Published January 3, 2019 | Version v1
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Statistical Stability for Transport in Random Media

Goudon, Thierry
Vasseur, Alexis
Others:
COmplex Flows For Energy and Environment (COFFEE) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Departement of Mathematics [Austin] ; University of Texas at Austin [Austin]

Description

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

Abstract

International audience

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Created:
December 4, 2022
Modified:
November 23, 2023