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Creators/Authors contains: "Schlag, W."

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  1. (, Journal of Mathematical Physics)
  2. ; (, American Journal of Mathematics)
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  3. ; ; (, Ergodic Theory and Dynamical Systems)
    We prove a conditional theorem on the positivity of the Lyapunov exponent for a Schrödinger cocycle over a skew-shift base with a cosine potential and the golden ratio as frequency. For coupling below $$1$$ , which is the threshold for Herman’s subharmonicity trick, we formulate three conditions on the Lyapunov exponent in a finite but large volume and on the associated large-deviation estimates at that scale. Our main results demonstrate that these finite-size conditions imply the positivity of the infinite-volume Lyapunov exponent. This paper shows that it is possible to make the techniques developed for the study of Schrödinger operators with deterministic potentials, based on large-deviation estimates and the avalanche principle, effective. 
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  4. ; ; ; (, Communications in Mathematical Physics)
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  5. ; ; ; (, American Journal of Mathematics)
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  6. ; ; ; (, American Journal of Mathematics)
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