{
  "id": "2106.06447",
  "version": "v1",
  "published": "2021-06-11T15:04:41.000Z",
  "updated": "2021-06-11T15:04:41.000Z",
  "title": "A functional central limit theorem for Polaron path measures",
  "authors": [
    "Volker Betz",
    "Steffen Polzer"
  ],
  "comment": "39 pages, 2 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The application of the Feynman-Kac formula to Polaron models of quantum theory leads to the path measure of Brownian motion perturbed by a pair potential that is translation invariant both in space and time. An important problem in this context is the validity of a central limit theorem in infinite volume. We show both the existence of the relevant infinite volume limits and a functional central limit theorem in a generality that includes the Fr\\\"ohlich polaron for all coupling constants. The proofs are based on an extension of a novel method by Mukherjee and Varadhan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-11T15:04:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F17",
      "60G55",
      "60K05",
      "81S40"
    ],
    "keywords": [
      "functional central limit theorem",
      "polaron path measures",
      "relevant infinite volume limits",
      "feynman-kac formula",
      "translation invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}