{
  "id": "1104.4268",
  "version": "v3",
  "published": "2011-04-21T14:03:47.000Z",
  "updated": "2012-10-25T16:14:18.000Z",
  "title": "Nonlinear PDEs for gap probabilities in random matrices and KP theory",
  "authors": [
    "M. Adler",
    "M. Cafasso",
    "P. van Moerbeke"
  ],
  "comment": "Minor revision: accepted for publication on Physica D",
  "journal": "Physica D, 241, 2012, 2265-2284",
  "doi": "10.1016/j.physd.2012.08.016",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR",
    "nlin.SI"
  ],
  "abstract": "Airy and Pearcey-like kernels and generalizations arising in random matrix theory are expressed as double integrals of ratios of exponentials, possibly multiplied with a rational function. In this work it is shown that such kernels are intimately related to wave functions for polynomial (Gel'fand-Dickey reductions) or rational reductions of the KP-hierarchy; their Fredholm determinant also satisfies linear PDEs (Virasoro constraints), yielding, in a systematic way, non-linear PDEs for the Fredholm determinant of such kernels. Examples include Fredholm determinants giving the gap probability of some infinite-dimensional diffusions, like the Airy process, with or without outliers, and the Pearcey process, with or without inliers.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-10-25T16:14:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gap probability",
      "kp theory",
      "nonlinear pdes",
      "random matrices",
      "fredholm determinant"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Physica D Nonlinear Phenomena",
      "year": 2012,
      "month": "Dec",
      "volume": 241,
      "number": "23-24",
      "pages": 2265
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012PhyD..241.2265A"
    }
  }
}