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• W3100685712 abstract "In this paper we study Kac's 1D particle system, consisting of the velocities of $N$ particles colliding at constant rate and randomly exchanging energies. We prove uniform (in time) propagation of chaos in Wasserstein distance with explicit polynomial rates in $N$, for both the squared (i.e., the energy) and non-squared particle system. These rates are of order $N^{-1/3}$ (almost, in the non-squared case), assuming that the initial distribution of the limit nonlinear equation has finite moments of sufficiently high order ($4+epsilon$ is enough when using the 2-Wasserstein distance). The proof relies on a convenient parametrization of the collision recently introduced by Hauray, as well as on a coupling technique developed by Cortez and Fontbona." @default.
• W3100685712 created "2020-11-23" @default.
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• W3100685712 date "2016-11-19" @default.
• W3100685712 modified "2023-10-02" @default.
• W3100685712 title "Uniform Propagation of Chaos for Kac’s 1D Particle System" @default.
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• W3100685712 doi "https://doi.org/10.1007/s10955-016-1674-x" @default.
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