Large deviation theorems for Dirichlet determinants of analytic quasi-periodic Jacobi operators with Brjuno-Rüssmann frequency

DOI10.3934/CPAA.2020240zbMath1462.37030arXiv1906.11136OpenAlexW3083073472MaRDI QIDQ2658683

Wenmeng Geng, Kai Tao

Publication date: 23 March 2021

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.11136

zbMATH Keywords

Jacobi operatorslarge deviation theoremsstrong Birkhoff ergodic theoremBrjuno-Rüssmann frequencyfinite scale Dirichlet determinants

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Periodic and quasi-periodic flows and diffeomorphisms (37C55)

Related Items (4)

Homogeneous spectrum of quasi-periodic Gevrey Schrödinger operators with Diophantine frequency ⋮ An inequality for imaginary parts of eigenvalues of non-compact operators with Hilbert-Schmidt Hermitian components ⋮ Variations of real and imaginary parts of eigenvalues of compact operators under perturbations ⋮ Lyapunov exponents of discrete quasi-periodic Gevrey Schrödinger equations

Cites Work

• Unnamed Item
• On resonances and the formation of gaps in the spectrum of quasi-periodic Schrödinger equations
• Continuity of the Lyapunov exponent for analytic quasi-periodic cocycles with singularities
• Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues
• Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential
• Homogeneity of the spectrum for quasi-periodic Schrödinger operators
• Sharp phase transitions for the almost Mathieu operator
• Localization for a family of one-dimensional quasiperiodic operators of magnetic origin
• An estimate on the number of eigenvalues of a quasiperiodic Jacobi matrix of size \(n\) contained in an interval of size \(n^{-C}\)
• The Ten Martini problem
• Full measure reducibility and localization for quasiperiodic Jacobi operators: a topological criterion
• On optimal separation of eigenvalues for a quasiperiodic Jacobi matrix
• Hölder continuity of the Lyapunov exponent for analytic quasiperiodic Schrödinger cocycle with weak Liouville frequency
• Continuity of the Lyapunov exponent for analytic quasiperiodic cocycles
• Dry Ten Martini problem for the non-self-dual extended Harper’s model
• H\"older continuity of Lyapunov exponent for quasi-periodic Jacobi operators
• On nonperturbative localization with quasi-periodic potential.
• Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions
• Anderson localization for Schrödinger operators on \(\mathbb Z\) with potentials given by the skew-shift

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