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We prove localization and probabilistic bounds on the minimum level spacing for a random block Anderson model without monotonicity. Using a sequence of narrowing energy windows and associated Schur complements, we obtain detailed probabilistic information about the microscopic structure of energy levels of the Hamiltonian, as well as the support and decay of eigenfunctions.
A new KAM-style proof of Anderson localization is obtained. A sequence of local rotations is defined, such that off-diagonal matrix elements of the Hamiltonian are driven rapidly to zero. This leads to the first proof via multi-scale analysis of expo
We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking N values, with N large.
We apply Feshbach-Krein-Schur renormalization techniques in the hierarchical Anderson model to establish a criterion on the single-site distribution which ensures exponential dynamical localization as well as positive inverse participation ratios and
For one-dimensional random Schrodinger operators, the integrated density of states is known to be given in terms of the (averaged) rotation number of the Prufer phase dynamics. This paper develops a controlled perturbation theory for the rotation num
We consider the Rosenzweig-Porter model $H = V + sqrt{T}, Phi$, where $V$ is a $N times N$ diagonal matrix, $Phi$ is drawn from the $N times N$ Gaussian Orthogonal Ensemble, and $N^{-1} ll T ll 1$. We prove that the eigenfunctions of $H$ are typicall