# Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases

@article{Guillin2022ConvergenceRF, title={Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases}, author={Arnaud Guillin and Pierre Le Bris and Pierre Monmarch'e}, journal={Electronic Journal of Probability}, year={2022} }

Abstract We prove the existence of a contraction rate for Vlasov-Fokker-Planck equation in Wasserstein distance, provided the interaction potential is (locally) Lipschitz continuous and the confining potential is both Lipschitz continuous and greater than a quadratic function, thus requiring no convexity conditions. Our strategy relies on coupling methods suggested by A. Eberle [Ebe16] adapted to the kinetic setting enabling also to obtain uniform in time propagation of chaos in a non convex…

## 4 Citations

### Exponential Entropy dissipation for weakly self-consistent Vlasov-Fokker-Planck equations

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. We study long-time dynamical behaviors of weakly self-consistent Vlasov-Fokker-Planck equations. We introduce Hessian matrix conditions on mean-ﬁeld kernel functions, which characterizes the…

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. This article introduces a novel approach to the mean-ﬁeld limit of stochastic systems of interacting particles, leading to the ﬁrst ever derivation of the mean-ﬁeld limit to the…

### Chaos propagation in mean field networks of FitzHugh-Nagumo neurons

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In this article, we are interested in the behavior of a fully connected network of N neurons, where N tends to inﬁnity. We assume that neurons follow the stochastic FitzHugh-Nagumo model, whose…

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We study the long-time behaviour of both the classical second-order Langevin dynamics and the nonlinear second-order Langevin dynamics of McKean-Vlasov type. By a coupling approach, we establish…

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