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arXiv · 1902.04642

Positive Lyapunov Exponents and a Large Deviation Theorem for Continuum Anderson Models, Briefly

Valmir Bucaj·David Damanik·Jake Fillman·Vitaly Gerbuz·Tom VandenBoom·Fengpeng Wang·Zhenghe Zhang
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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.

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Valmir Bucaj, David Damanik, Jake Fillman, Vitaly Gerbuz, Tom VandenBoom, Fengpeng Wang, Zhenghe Zhang. 2019-02-12. Positive Lyapunov Exponents and a Large Deviation Theorem for Continuum Anderson Models, Briefly. https://arxiv.org/abs/1902.04642

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