Hölder continuity of the integrated density of states for Liouville frequencies
Abstract
We prove Hölder continuity of the Lyapunov exponent L(\omega,E) and of the integrated density of states in neighborhoods of energies that satisfy L(\omega,E)>4\kappa(\omega,E)\cdot \beta(\omega)\geq 0 for general analytic potentials, with \kappa(\omega,E) being Avila’s acceleration, and \beta(\omega) measures the closeness of \omega to rationals on a logarithmic scale.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Quantum Mechanics and Non-Hermitian Physics
Mathematical functions and polynomials
Publication details
- Journal / source
- Journal of Spectral Theory
- Publisher
- European Mathematical Society - EMS - Publishing House GmbH
- Volume
- 16
- Issue
- 3
- Pages
- 1081–1108
- Publication date
- 4 February 2026