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Multiscale analysis for ergodic schrödinger operators and positivity of Lyapunov exponents

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Abstract

A variant of multiscale analysis for ergodic Schrödinger operators is developed. This enables us to prove positivity of Lyapunov exponents, given initial scale estimates and an initial Wegner estimate. This postivivity is then applied to high-dimensional skew-shifts at small coupling, where initial conditions are checked using the Pastur-Figotin formalism.

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Author notes

  1. Helge Krüger

    Present address: , 1200 E California Blvd, Pasadena, CA, 91125, USa

Authors and Affiliations

  1. Department of Mathematics, Rice University, Houston, TX, 77005, USA

    Helge Krüger

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  1. Helge Krüger
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Correspondence to Helge Krüger.

Additional information

H. K. was supported by NSF grant DMS-0800100 and a Nettie S. Autrey Fellowship.

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Krüger, H. Multiscale analysis for ergodic schrödinger operators and positivity of Lyapunov exponents. JAMA 115, 343–387 (2011). https://doi.org/10.1007/s11854-011-0032-9

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  • DOI: https://doi.org/10.1007/s11854-011-0032-9

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