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Large Deviation Estimates and Hölder Regularity of the Lyapunov Exponents for Quasi-periodic Schrödinger Cocycles
International Mathematics Research Notices ( IF 1.452 ) Pub Date : 2020-05-21 , DOI: 10.1093/imrn/rnz319
Rui Han; Shiwen Zhang

We consider one-dimensional quasi-periodic Schrödinger operators with analytic potentials. In the positive Lyapunov exponent regime, we prove large deviation estimates, which lead to refined Hölder continuity of the Lyapunov exponents and the integrated density of states, in both small Lyapunov exponent and large coupling regimes. Our results cover all the Diophantine frequencies and some Liouville frequencies.
更新日期:2020-05-21

 

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