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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.07607 |
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Table of Contents:
- In this paper, we prove Hölder continuity of the integrated density of states for discrete quasiperiodic Jacobi $d\times d$ block matrices with Diophantine frequencies. The Hölder exponent is shown to be any $β$ such that $0<β<1/(2κ^d)$, where $κ^d$ is the acceleration, i.e., the slope of the sum of the top $d$ Lyapunov exponents in the imaginary direction of the phase. This generalizes the Hölder continuity results in the Schrödinger operator setting in \cites{GS2,HS1}, and also strengthens them in that setting by covering more Diophantine frequencies. The proof is built on a new scheme for obtaining a local zero count for finite-volume characteristic polynomials from a global one.