{
  "id": "math-ph/0411057",
  "version": "v1",
  "published": "2004-11-17T11:47:20.000Z",
  "updated": "2004-11-17T11:47:20.000Z",
  "title": "Polynuclear growth model, GOE$^2$ and random matrix with deterministic source",
  "authors": [
    "T. Imamura",
    "T. Sasamoto"
  ],
  "comment": "27pages, 4 figures",
  "journal": "Phys. Rev. E 71, 041606 (2005)",
  "doi": "10.1103/PhysRevE.71.041606",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP",
    "math.PR",
    "nlin.SI"
  ],
  "abstract": "We present a random matrix interpretation of the distribution functions which have appeared in the study of the one-dimensional polynuclear growth (PNG) model with external sources. It is shown that the distribution, GOE$^2$, which is defined as the square of the GOE Tracy-Widom distribution, can be obtained as the scaled largest eigenvalue distribution of a special case of a random matrix model with a deterministic source, which have been studied in a different context previously. Compared to the original interpretation of the GOE$^2$ as ``the square of GOE'', ours has an advantage that it can also describe the transition from the GUE Tracy-Widom distribution to the GOE$^2$. We further demonstrate that our random matrix interpretation can be obtained naturally by noting the similarity of the topology between a certain non-colliding Brownian motion model and the multi-layer PNG model with an external source. This provides us with a multi-matrix model interpretation of the multi-point height distributions of the PNG model with an external source.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-17T11:47:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynuclear growth model",
      "deterministic source",
      "random matrix interpretation",
      "external source",
      "png model"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}