Quantitative inductive estimates for Green's functions of non-self-adjoint matrices
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Publication:6344222
DOI10.2140/APDE.2022.15.2061arXiv2007.00578MaRDI QIDQ6344222
Publication date: 1 July 2020
Abstract: We provide quantitative inductive estimates for Green's functions of matrices with (sub)expoentially decaying off diagonal entries in higher 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 quasi-periodic operators. Moreover, our inductions are self-improved and work for perturbations with low complexity interactions.
Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Periodic and quasi-periodic flows and diffeomorphisms (37C55)
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