{
  "id": "1612.00321",
  "version": "v1",
  "published": "2016-12-01T15:48:55.000Z",
  "updated": "2016-12-01T15:48:55.000Z",
  "title": "Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes",
  "authors": [
    "Alexei Borodin",
    "Ivan Corwin",
    "Patrik L. Ferrari"
  ],
  "comment": "56 pages, 15 figures",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a discrete model for anisotropic (2+1)-dimensional growth of an interface height function. Owing to a connection with q-Whittaker functions, this system enjoys many explicit integral formulas. By considering certain Gaussian stochastic differential equation limits of the model we are able to prove a space-time limit to the (2+1)-dimensional additive stochastic heat equation (or Edwards-Wilkinson equation) along characteristic directions. In particular, the bulk height function converges to the Gaussian free field which evolves according to this stochastic PDE.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-01T15:48:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "q-whittaker processes",
      "gaussian limits",
      "anisotropic",
      "gaussian stochastic differential equation limits",
      "bulk height function converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}