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arXiv · 1902.00602

Geometric ergodicity of Langevin dynamics with Coulomb interactions

Yulong Lu·Jonathan C. Mattingly
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Abstract

This paper is concerned with the long time behavior of Langevin dynamics of {\em Coulomb gases} in $\mathbf{R}^d$ with $d\geq 2$, that is a second order system of Brownian particles driven by an external force and a pairwise repulsive Coulomb force. We prove that the system converges exponentially to the unique Boltzmann-Gibbs invariant measure under a weighted total variation distance. The proof relies on a novel construction of Lyapunov function for the Coulomb system.

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BibTeXRIS

Yulong Lu, Jonathan C. Mattingly. 2019-02-02. Geometric ergodicity of Langevin dynamics with Coulomb interactions. https://doi.org/10.1088/1361-6544/ab514a

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