{
  "id": "1904.03253",
  "version": "v1",
  "published": "2019-04-05T19:56:30.000Z",
  "updated": "2019-04-05T19:56:30.000Z",
  "title": "Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions",
  "authors": [
    "Will FitzGerald",
    "Jon Warren"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper proves an equality in law between the invariant measure of a reflected system of Brownian motions and a vector of point-to-line last passage percolation times in a discrete random environment. A consequence describes the distribution of the all-time supremum of Dyson Brownian motion with drift. A finite temperature version relates the point-to-line partition functions of two directed polymers, with an inverse-gamma and a Brownian environment, and generalises Dufresne's identity. Our proof introduces an interacting system of Brownian motions with an invariant measure given by a field of point-to-line log partition functions for the log-gamma polymer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-05T19:56:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60B20",
      "60K35"
    ],
    "keywords": [
      "invariant measure",
      "reflecting brownian motions",
      "point-to-line log partition functions",
      "finite temperature version relates",
      "dyson brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}