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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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| _version_ | 1866914160970825728 |
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| author | Han, Rui Schlag, Wilhelm |
| author_facet | Han, Rui Schlag, Wilhelm |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hölder continuity of the integrated density of states for quasi-periodic Jacobi block matrices Han, Rui Schlag, Wilhelm Spectral Theory Mathematical Physics Dynamical Systems 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. |
| title | Hölder continuity of the integrated density of states for quasi-periodic Jacobi block matrices |
| topic | Spectral Theory Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2511.07607 |