H\"older Continuity of the Integrated Density of States for the Fibonacci Hamiltonian

TL;DR

This paper proves that the integrated density of states for the Fibonacci Hamiltonian is H"older continuous for all positive couplings and analyzes how the H"older exponents behave as the coupling varies.

Contribution

It establishes H"older continuity for the integrated density of states across all positive couplings and derives asymptotic behavior of the H"older exponents for extreme coupling values.

Findings

H"older continuity holds for all positive couplings.

Asymptotic behavior of H"older exponents characterized for large and small couplings.

Provides a detailed analysis of the regularity of the integrated density of states.

Abstract

We prove H\"older continuity of the integrated density of states for the Fibonacci Hamiltonian for any positive coupling, and obtain the asymptotics of the H\"older exponents for large and small couplings.