{
  "id": "2105.03107",
  "version": "v1",
  "published": "2021-05-07T08:23:13.000Z",
  "updated": "2021-05-07T08:23:13.000Z",
  "title": "New characterization of the weak disorder phase of directed polymers in bounded random environments",
  "authors": [
    "Stefan Junk"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that the weak disorder phase for the directed polymer model in a bounded random environment is characterized by the integrability of the running supremum $\\sup_{n\\in \\mathbb N}W_n^\\beta$ of the associated martingale $(W_n^\\beta)_{n\\in \\mathbb N}$. Using this characterization, we prove that $(W_n^\\beta)_{n\\in \\mathbb N}$ is $L^p$-bounded in the whole weak disorder phase, for some $p>1$. The argument generalizes to non-negative martingales with a certain product structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-07T08:23:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37"
    ],
    "keywords": [
      "weak disorder phase",
      "bounded random environment",
      "characterization",
      "directed polymer model",
      "argument generalizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}