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

@article{Liu2020QuantitativeIE, title={Quantitative inductive estimates for Green's functions of non-self-adjoint matrices}, author={Wencai Liu}, journal={arXiv: Mathematical Physics}, year={2020} }

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…

## 12 Citations

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Summary: We present a simple method, not based on the transfer matrices, to prove vanishing of dynamical transport exponents. The method is applied to long-range quasiperiodic operators.

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