{
  "id": "1909.07962",
  "version": "v1",
  "published": "2019-09-17T17:52:48.000Z",
  "updated": "2019-09-17T17:52:48.000Z",
  "title": "Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions",
  "authors": [
    "Nawaf Bou-Rabee",
    "Andreas Eberle"
  ],
  "comment": "36 pages, 4 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We derive non-asymptotic quantitative bounds for convergence to equilibrium of the exact preconditioned Hamiltonian Monte Carlo algorithm (pHMC) on a Hilbert space. As a consequence, explicit and dimension-free bounds for pHMC applied to high-dimensional distributions arising in transition path sampling and path integral molecular dynamics are given. Global convexity of the underlying potential energies is not required. Our results are based on a two-scale coupling which is contractive in a carefully designed distance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-17T17:52:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J05",
      "60B12",
      "60J22",
      "65P10",
      "65C05",
      "65C40"
    ],
    "keywords": [
      "infinite dimensions",
      "two-scale coupling",
      "preconditioned hamiltonian monte carlo algorithm",
      "path integral molecular dynamics",
      "exact preconditioned hamiltonian monte carlo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}