title

Delocalization of eigenvectors of random matrices with independent entries

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Duke Mathematical Journal

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citation_journal_title

Duke Mathematical Journal

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Paper

og:url

https://projecteuclid.org/journals/duke-mathematical-journal/volume-164/issue-13/Delocalization-of-eigenvectors-of-random-matrices-with-independent-entries/10.1215/00127094-3129809.full

og:title

Delocalization of eigenvectors of random matrices with independent entries

og:description

We prove that an n×n random matrix G with independent entries is completely delocalized. Suppose that the entries of G have zero means, variances uniformly bounded below, and a uniform tail decay of exponential type. Then with high probability all unit eigenvectors of G have all coordinates of magnitude O(n−1/2), modulo logarithmic corrections. This comes as a consequence of a new, geometric approach to delocalization for random matrices.

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2015-10-01T00:00:00-07:00

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