Communications in Mathematical Physics

, Volume 90, Issue 2, pp 207–218 | Cite as

Log hölder continuity of the integrated density of states for stochastic Jacobi matrices

  • Walter Craig
  • Barry Simon


We consider the integrated density of states,k(E), of a general operator on ℓ2(ℤv) of the formh=h0+v, where\((h_0 u)(n) = \sum\limits_{\left| i \right| = 1} {u(n + i)} \) and (vu)(n)=v(n)u(n), wherev is a general bounded ergodic stationary process on ℤv. We show that |k(E)−k(E′)|≦C[−log(|EE′|]−1 when |EE′|≦1/2, The key is a “Thouless formula for the strip.”


Neural Network Statistical Physic Complex System Stationary Process Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Walter Craig
    • 1
  • Barry Simon
    • 1
  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA

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