{
  "id": "math/0409013",
  "version": "v1",
  "published": "2004-09-01T11:38:41.000Z",
  "updated": "2004-09-01T11:38:41.000Z",
  "title": "Non-intersecting, simple, symmetric random walks and the extended Hahn kernel",
  "authors": [
    "Kurt Johansson"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Consider $a$ particles performing simple, symmetric, non-intersecting random walks, starting at points $2(j-1)$, $1\\le j\\le a$ at time 0 and ending at $2(j-1)+c-b$ at time $b+c$. This can also be interpreted as a random rhombus tiling of an $abc$-hexagon, or as a random boxed planar partition confined to a rectangular box with side lengths $a$, $b$ and $c$. The positions of the particles at all times gives a determinantal point process with a correlation kernel given in terms of the associated Hahn polynomials. In a suitable scaling limit we obtain non-intersecting Brownian motions which can be related to Dysons's Hermitian Brownian motion via a suitable transformation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-01T11:38:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "15A32"
    ],
    "keywords": [
      "symmetric random walks",
      "extended hahn kernel",
      "boxed planar partition",
      "dysonss hermitian brownian motion",
      "non-intersecting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9013J"
    }
  }
}