{
  "id": "1902.00602",
  "version": "v1",
  "published": "2019-02-02T01:00:04.000Z",
  "updated": "2019-02-02T01:00:04.000Z",
  "title": "Geometric ergodicity of Langevin dynamics with Coulomb interactions",
  "authors": [
    "Yulong Lu",
    "Jonathan C. Mattingly"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.DS",
    "math.MP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-02T01:00:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "langevin dynamics",
      "coulomb interactions",
      "geometric ergodicity",
      "unique boltzmann-gibbs invariant measure",
      "second order system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}