Delocalization of eigenvectors of random matrices with independent entries

Mark Rudelson; Roman Vershynin

doi:10.1215/00127094-3129809

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arXiv · 1306.2887

Delocalization of eigenvectors of random matrices with independent entries

Mark Rudelson·Roman Vershynin

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Abstract

We prove that an n by n random matrix G with independent entries is completely delocalized. Suppose 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 a consequence of a new, geometric, approach to delocalization for random matrices.

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Mark Rudelson, Roman Vershynin. 2013-06-12. Delocalization of eigenvectors of random matrices with independent entries. https://doi.org/10.1215/00127094-3129809

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