Large deviation estimates and Hölder regularity of the Lyapunov exponents for quasi-periodic Schrödinger cocycles

Abstract

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 optimal 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.

arXiv commentInternational Mathematics Research Notices

References in corpus (7)

• Dynamics and spectral theory of quasi-periodic Schrödinger-type operators
• Complex one-frequency cocycles
• Continuity of the Lyapunov exponents for quasiperiodic cocycles
• Localization for quasiperiodic Schrodinger operators with multivariable Gevrey potential functions
• Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent
• Sharp Holder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles
• Large deviations for quasi-periodic cocycles with singularities

Cited by in corpus (4)

• Quantitative inductive estimates for Green's functions of non-self-adjoint matrices
• Transition space for the continuity of the Lyapunov exponent of quasiperiodic Schrödinger cocycles
• Strong Birkhoff Ergodic Theorem for subharmonic functions with irrational shift and its application to analytic quasi-periodic cocycles
• Large Deviation theorems for Dirichlet determinants of analytic quasi-periodic Jacobi operators with Brjuno-Rüssmann frequency