{
  "id": "math-ph/0703060",
  "version": "v1",
  "published": "2007-03-20T16:00:35.000Z",
  "updated": "2007-03-20T16:00:35.000Z",
  "title": "Positivity of Lyapunov exponents for a continuous matrix-valued Anderson model",
  "authors": [
    "H. Boumaza"
  ],
  "journal": "Math. Phys. Anal. Geom. 10 (2), 97-122 (2007)",
  "doi": "10.1007/s11040-007-9023-6",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We study a continuous matrix-valued Anderson-type model. Both leading Lyapunov exponents of this model are proved to be positive and distinct for all ernergies in $(2,+\\infty)$ except those in a discrete set, which leads to absence of absolutely continuous spectrum in $(2,+\\infty)$. This result is an improvement of a previous result with Stolz. The methods, based upon a result by Breuillard and Gelander on dense subgroups in semisimple Lie groups, and a criterion by Goldsheid and Margulis, allow for singular Bernoulli distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-20T16:00:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous matrix-valued anderson model",
      "lyapunov exponents",
      "positivity",
      "semisimple lie groups",
      "singular bernoulli distributions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}