{
  "id": "1711.02250",
  "version": "v1",
  "published": "2017-11-07T01:42:13.000Z",
  "updated": "2017-11-07T01:42:13.000Z",
  "title": "Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials",
  "authors": [
    "David P. Herzog",
    "Jonathan C. Mattingly"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.DS",
    "math.MP"
  ],
  "abstract": "We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the well-known Lennard-Jones type, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted total variation distance. The proof of the main result relies on an explicit construction of a Lyapunov function. In contrast to previous results for such systems, our result implies geometric convergence to equilibrium starting from an essentially optimal family of initial distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-07T01:42:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "82C31",
      "37A25",
      "37B25"
    ],
    "keywords": [
      "lyapunov function",
      "langevin dynamics",
      "singular potentials",
      "unique invariant gibbs measure",
      "ergodicity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}