Quantitative inductive estimates for Green's functions of non-self-adjoint matrices

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.

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Cited by in corpus (6)

• Upper bounds on transport exponents for long range operators
• Quantitative Green's Function Estimates for Lattice Quasi-periodic Schrödinger Operators
• Power law logarithmic bounds of moments for long range operators in arbitrary dimension
• Bethe-Sommerfeld Conjecture and Absolutely Continuous Spectrum of Multi-Dimensional Quasi-Periodic Schrödinger Operators
• Absence of eigenvalues of analytic quasi-periodic Schrodinger operators on ${\mathbb{R}}^d$
• A "lifting" method for exponential large deviation estimates and an application to certain non-stationary 1D lattice Anderson models