An extension of Kotani's theorem to random generalized Sturm-Liouville operators

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We consider the random operator: -d/mω(dx)d+/dx+qω(x), where mω(dx) and qω(x) are a stationary ergodic random measure and a random function respectively. To this general case, we extend Kotani's theorem which asserts that the absolutely continuous spectrum is completely determined by the Ljapounov indices. Our framework includes the case of stochastic Jacobi matrices treated by Simon.

Original languageEnglish
Pages (from-to)387-402
Number of pages16
JournalCommunications in Mathematical Physics
Issue number3
Publication statusPublished - 1986 Sep 1
Externally publishedYes


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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