Eigenvector Localization for Random Band Matrices with Power Law Band Width |
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Authors: | Jeffrey Schenker |
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Institution: | (1) Michigan State University, East Lansing, Michigan, 48824, USA |
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Abstract: | It is shown that certain ensembles of random matrices with entries that vanish outside a band around the diagonal satisfy
a localization condition on the resolvent which guarantees that eigenvectors have strong overlap with a vanishing fraction
of standard basis vectors, provided the band width W raised to a power μ remains smaller than the matrix size N. For a Gaussian band ensemble, with matrix elements given by i.i.d. centered Gaussians within a band of width W, the estimate μ ≤ 8 holds. |
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Keywords: | |
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