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Quantitative Uniform Propagation of Chaos for Maxwell Molecules

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Abstract

We prove propagation of chaos at explicit polynomial rates in Wasserstein distance \({\mathcal{W}_{2}}\) for Kac’s N-particle system associated with the spatially homogeneous Boltzmann equation for Maxwell molecules. Our approach is mainly based on novel probabilistic coupling techniques. Combining them with recent stabilization results for the particle system we obtain, under suitable moments assumptions on the initial distribution, a uniform-in-time estimate of order almost \({N^{-1/3}}\) for \({\mathcal{W}_{2}^{2}}\) .

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Authors and Affiliations

  1. CIMFAV, Facultad de Ingenieria, Universidad de Valparaíso, General Cruz 222, Valparaiso, Chile

    Roberto Cortez

  2. Department of Mathematical Engineering and Center for Mathematical Modeling, UMI(2807) UCHILE-CNRS, University of Chile, Casilla 170-3, Correo 3, Santiago, Chile

    Joaquin Fontbona

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  1. Roberto Cortez
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  2. Joaquin Fontbona
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Correspondence to Joaquin Fontbona.

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Communicated by C. Mouhot

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Cortez, R., Fontbona, J. Quantitative Uniform Propagation of Chaos for Maxwell Molecules. Commun. Math. Phys. 357, 913–941 (2018). https://doi.org/10.1007/s00220-018-3101-4

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