Positive Lyapunov Exponents and a Large Deviation Theorem for Continuum Anderson Models, Briefly
Spectral Theory
2019-03-08 v2 Mathematical Physics
Dynamical Systems
math.MP
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.
Keywords
Cite
@article{arxiv.1902.04642,
title = {Positive Lyapunov Exponents and a Large Deviation Theorem for Continuum Anderson Models, Briefly},
author = {Valmir Bucaj and David Damanik and Jake Fillman and Vitaly Gerbuz and Tom VandenBoom and Fengpeng Wang and Zhenghe Zhang},
journal= {arXiv preprint arXiv:1902.04642},
year = {2019}
}
Comments
5 pages; added a discussion of a one-parameter reformulation of F\"urstenberg's Theorem in v2