On Optimal Separation of Eigenvalues for a Quasiperiodic Jacobi Matrix

Abstract

We consider quasiperiodic Jacobi matrices of size N with analytic coefficients. We show that, in the positive Lyapunov exponent regime, after removing some small sets of energies and frequencies, any eigenvalue is separated from the rest of the spectrum by $N^{-1}(\log N{)}^{-p}$, with p>15.

45 pages

References in corpus (1)

• Continuity of the Lyapunov Exponent for analytic quasi-perodic cocycles with singularities

Cited by in corpus (3)

• Dynamics and spectral theory of quasi-periodic Schrödinger-type operators
• Dominated splittings and the spectrum of singular quasi-periodic Jacobi operators
• Hölder continuity of the integrated density of states for quasi-periodic Jacobi operators