{
  "id": "0907.4929",
  "version": "v1",
  "published": "2009-07-28T15:06:45.000Z",
  "updated": "2009-07-28T15:06:45.000Z",
  "title": "Random matrices and Laplacian growth",
  "authors": [
    "A. Zabrodin"
  ],
  "comment": "20 pages, 2 figures, a contribution to the Oxford Handbook of Random Matrix Theory",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The theory of random matrices with eigenvalues distributed in the complex plane and more general \"beta-ensembles\" (logarithmic gases in 2D) is reviewed. The distribution and correlations of the eigenvalues are investigated in the large N limit. It is shown that in this limit the model is mathematically equivalent to a class of diffusion-controlled growth models for viscous flows in the Hele-Shaw cell and other growth processes of Laplacian type. The analytical methods used involve the technique of boundary value problems in two dimensions and elements of the potential theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-28T15:06:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random matrices",
      "laplacian growth",
      "boundary value problems",
      "eigenvalues",
      "complex plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.4929Z"
    }
  }
}