Article
Preprint
Multiscale Analysis for Ergodic Schrödinger operators and positivity of Lyapunov exponents
Helge Krüger
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 is then applied to high dimensional skew-shifts at small coupling,
where initial conditions are checked using the Pastur-Figotin formalism.
Furthermore, it is shown that for potentials generated by the doubling
map one has positive Lyapunov exponent except in a superpolynomially small
set.
MSC2000: Primary 81Q10; Secondary 37D25
Keywords: Lyapunov Exponents, Schrödinger Operators