Positive Lyapunov Exponents and a Large Deviation Theorem for Continuum Anderson Models, Briefly
Abstract
In this short note, we prove positivity of the Lyapunov exponent for 1D continuum Anderson models by leveraging some classical tools from inverse spectral theory. The argument is much simpler than the existing proof due to Damanik--Sims--Stolz, and it covers a wider variety of random models. Along the way we note that a Large Deviation Theorem holds uniformly on compacts.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2019
- DOI:
- arXiv:
- arXiv:1902.04642
- Bibcode:
- 2019arXiv190204642B
- Keywords:
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- Mathematics - Spectral Theory;
- Mathematical Physics;
- Mathematics - Dynamical Systems
- E-Print:
- 5 pages