Published June 2011
| public
Journal Article
Multiscale analysis for ergodic Schrödinger operators and positivity of Lyapunov exponents
- Creators
- Krüger, Helge
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.
Additional Information
© 2011 Springer, Part of Springer Science+Business Media. Received July 22, 2010. H. K. was supported by NSF grant DMS–0800100 and a Nettie S. Autrey Fellowship. I thank Daniel Lenz and Günter Stolz for their help when I started learning about these problems. I am indebted to David Damanik for useful advice and suggestions, and to Jon Chaika for useful conversations. Lastly, I thank Jean Bourgain and Svetlana Jitomirskaya for help with the literature.Additional details
- Eprint ID
- 29698
- Resolver ID
- CaltechAUTHORS:20120313-102043175
- DMS–0800100
- NSF
- Nettie S. Autrey Fellowship
- Created
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2012-03-13Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field