Hölder Regularity of Integrated Density of States for the Almost Mathieu Operator in a Perturbative Regime

By Jean Bourgain. 2000

56 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9b082f2eab633a2fe9bd9a5868ba1a9adb6a002f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Artur Avila
2. S. Jitomirskaya
3. Jean Bourgain
4. David Damanik

In Mathematical Physics

1. Artur Avila
2. S. Jitomirskaya
3. David Damanik
4. Jiangong You
5. Jean Bourgain
6. Qi Zhou
7. Marcelo Viana
8. R. Krikorian

In Statistical and Nonlinear Physics

1. Artur Avila
2. S. Jitomirskaya
3. Jean Bourgain
4. David Damanik
5. Jiangong You
6. Qi Zhou
7. R. Krikorian
8. Marcelo Viana

Citations in the corpus

• Continuity of the Lyapunov Exponent for Quasiperiodic Operators with Analytic Potential (2001, background): “Precise estimates on Hölder regularity for the almost Mathieu operator at high coupling are contained in [4].”
• Almost localization and almost reducibility (2008, background): “ subset of Diophantine frequencies (they are also able to consider other analytic functions, in the regime of positive Lyapunov exponent, at the cost of a worse Ho¨lder constant). Previously Bourgain [B1] had obtained almost 1/2-Ho¨lder continuity in the perturbative regime, for Diophantine αand ln|”