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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