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

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Abstract

We consider the integrated density of states,k(E), of a general operator on ℓ2(ℤv) of the formh=h 0+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(|E−E′|]−1 when |E−E′|≦1/2, The key is a “Thouless formula for the strip.”

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Authors and Affiliations

  1. Department of Mathematics, California Institute of Technology, 91125, Pasadena, CA, USA

    Walter Craig & Barry Simon

Authors
  1. Walter Craig
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  2. Barry Simon
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Additional information

Communicated by T. Spencer

Also at Department of Physics, Research partially supported by USNSF Grant MCS-81-20833

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Craig, W., Simon, B. Log hölder continuity of the integrated density of states for stochastic Jacobi matrices. Commun.Math. Phys. 90, 207–218 (1983). https://doi.org/10.1007/BF01205503

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  • DOI: https://doi.org/10.1007/BF01205503

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