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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
Article

Abstract

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.”

Keywords

Neural Network Statistical Physic Complex System Stationary Process Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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