{
  "id": "2307.05097",
  "version": "v1",
  "published": "2023-07-11T08:11:22.000Z",
  "updated": "2023-07-11T08:11:22.000Z",
  "title": "Local limit theorem for directed polymers beyond the $L^2$-phase",
  "authors": [
    "Stefan Junk"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the directed polymer model in the weak disorder phase under the assumption that the partition function is $L^p$-bounded for some $p>1+2/d$. We prove a local limit theorem for the polymer measure, i.e., that the point-to-point partition function can be approximated by two point-to-plane partition functions at the start- and endpoint. We furthermore show that for environments with finite support the required $L^p$-boundedness holds in the whole weak disorder phase, except possible for the critical value $\\beta_{cr}$. Some consequences of the local limit theorem are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-11T08:11:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37"
    ],
    "keywords": [
      "local limit theorem",
      "weak disorder phase",
      "point-to-point partition function",
      "point-to-plane partition functions",
      "directed polymer model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}