{
  "id": "1205.3396",
  "version": "v2",
  "published": "2012-05-15T14:39:43.000Z",
  "updated": "2013-01-08T11:03:33.000Z",
  "title": "Existence of a unique strong solution to the DMPK equation",
  "authors": [
    "Maximilian Butz"
  ],
  "comment": "27 pages; version2: 28 pages, error in equation (2) corrected",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "For the transmission of electrons in a weakly disordered strip of material Dorokhov, Mello, Pereyra and Kumar (DMPK) proposed a diffusion process for the transfer matrices. The correspoding transmission eigenvalues satisfy the DMPK stochastic differential equations, like Dyson Brownian motion in the context of GOE/GUE random matrices. We control the singular repulsion terms of this SDE with a stopping-time argument, and its degenerate initial condition by an approximation procedure, and thereby establish the DMPK equation to be well posed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-08T11:03:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "60H10",
      "60K35",
      "82D77"
    ],
    "keywords": [
      "unique strong solution",
      "dmpk equation",
      "dmpk stochastic differential equations",
      "correspoding transmission eigenvalues satisfy",
      "dyson brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.3396B"
    }
  }
}