This article demonstrates convergence in kinetic Fokker-Planck equations, with implications for non-explicit steady states and fat-tailed local equilibria.
In this article, we prove some convergence results for kinetic Fokker-Planck equations with strong space confinement but fat-tailed local equilibria and non-explicit global steady states. We extend the results of {C21} to a wider class of fat-tailed local equilibria, with rates of convergence in a large class of weighted ¹ spaces. We complement our results with numerical simulations to investigate the shape of the non-explicit steady state.
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Bouin et al. (2025) studied this question.
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