Bounds on the density of states of random Schrödinger operators

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Bounds are obtained on the unintegrated density of states ρ(E) of random Schrödinger operators H=-Δ + V acting on L2(ℝd) or l2(ℤd). In both cases the random potential is {Mathematical expression}in which the {Mathematical expression} are IID random variables with density f. The χ denotes indicator function, and in the continuum case the {Mathematical expression} are cells of unit dimensions centered on y∈ℤd. In the finite-difference case Λ(y) denotes the site y∈ℤd itself. Under the assumption f ∈ L01+e{open}(ℝ) it is proven that in the finitedifference case p ∈ L(ℝ), and that in the d= 1 continuum case p ∈ Lloc(ℝ).

Original languageEnglish (US)
Pages (from-to)425-447
Number of pages23
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - Aug 1987


  • Random operators
  • Schrödinger equation
  • density of states

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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