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Random band matrix localization by scalar fluctuations
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We show the eigenvectors of a Gaussian random band matrix are localized when the band width is less than the 1/4 power of the matrix size. Our argument is essentially an optimized version of Schenker's proof of the 1/8 exponent.
Forward citations
Cited by 3 Pith papers
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On a Rosenzweig-Porter-type model
Uniform single- and two-resolvent local laws for arbitrary deformations of Wigner matrices yield ETH and localization profiles for all λ and H0.
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The Zigzag Strategy for Random Band Matrices
For random band matrices with width W >> sqrt(N), the paper proves complete delocalization, Wigner-Dyson statistics, and quantum unique ergodicity for general distributions and variance profiles.
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Delocalization of One-Dimensional Random Band Matrices
For one-dimensional block band matrices with W > N^{1/2+c}, the paper proves the local semicircle law, eigenvector delocalization, quantum unique ergodicity, and GUE universality.
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