{
  "id": "1005.4083",
  "version": "v6",
  "published": "2010-05-21T21:22:17.000Z",
  "updated": "2011-03-31T03:04:05.000Z",
  "title": "The transition between the gap probabilities from the Pearcey to the Airy process; a Riemann-Hilbert approach",
  "authors": [
    "M. Bertola",
    "M. Cafasso"
  ],
  "comment": "43 pages, 7 figures. Final version with minor changes. Accepted for publication on International Mathematical Research Notices",
  "journal": "Int Math Res Notices (2012) Vol. 2012 1519-1568",
  "doi": "10.1093/imrn/rnr066",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We consider the gap probability for the Pearcey and Airy processes; we set up a Riemann--Hilbert approach (different from the standard one) whereby the asymptotic analysis for large gap/large time of the Pearcey process is shown to factorize into two independent Airy processes using the Deift-Zhou steepest descent analysis. Additionally we relate the theory of Fredholm determinants of integrable kernels and the theory of isomonodromic tau function. Using the Riemann-Hilbert problem mentioned above we construct a suitable Lax pair formalism for the Pearcey gap probability and re-derive the two nonlinear PDEs recently found and additionally find a third one not reducible to those.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2011-03-31T03:04:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann-hilbert approach",
      "transition",
      "deift-zhou steepest descent analysis",
      "suitable lax pair formalism",
      "isomonodromic tau function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.4083B"
    }
  }
}