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Quantitative
inductive estimates for Green's functions of non-self-adjoint
matrices
Wencai Liu |
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Vol. 15 (2022), No. 8, 2061–2108
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Abstract |
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We provide quantitative inductive estimates for Green’s functions of matrices with (sub-)exponentially decaying off-diagonal entries in arbitrary dimensions. Together with Cartan’s estimates and discrepancy estimates, we establish explicit bounds for the large-deviation theorem for non-self-adjoint Toeplitz operators. As applications, we obtain the modulus of continuity of the integrated density of states with explicit bounds and the pure point spectrum property for analytic quasiperiodic operators. Moreover, our inductions are self-improved and work for perturbations with low-complexity interactions. |
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Keywords
multiscale analysis, large-deviation theorem, discrepancy,
semialgebraic sets, Cartan's techniques, Anderson
localization
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Mathematical Subject Classification
Primary: 81Q10
Secondary: 37C55, 82B44
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Milestones
Received: 24 September 2020
Revised: 29 March 2021
Accepted: 19 May 2021
Published: 10 February 2023
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Authors |
| Wencai Liu | |
| Department of Mathematics Texas A&M University College Station, TX United States |
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