{
  "id": "2303.04224",
  "version": "v2",
  "published": "2023-03-07T20:34:06.000Z",
  "updated": "2023-03-16T19:43:09.000Z",
  "title": "Differentiability of the Shape Function for Directed Polymers in Continuous Space",
  "authors": [
    "Yuri Bakhtin",
    "Douglas Dow"
  ],
  "comment": "Minor changes in this version, adding a couple remarks and correcting a few typos. 28 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "For directed polymers, the shape function computes the limiting average energy accrued by paths with a given average slope. We prove that, for a large family of directed polymer models in discrete time and continuous space in dimension $1+1$, for positive and zero temperature, the shape function is differentiable with respect to the slope on the entire real line.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-03-16T19:43:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37",
      "82B44",
      "82D60"
    ],
    "keywords": [
      "shape function",
      "continuous space",
      "differentiability",
      "entire real line",
      "directed polymer models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}