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1 October 2015 Delocalization of eigenvectors of random matrices with independent entries
Mark Rudelson, Roman Vershynin
Duke Math. J. 164(13): 2507-2538 (1 October 2015). DOI: 10.1215/00127094-3129809

Abstract

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(n1/2), modulo logarithmic corrections. This comes as a consequence of a new, geometric approach to delocalization for random matrices.

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Mark Rudelson. Roman Vershynin. "Delocalization of eigenvectors of random matrices with independent entries." Duke Math. J. 164 (13) 2507 - 2538, 1 October 2015. https://doi.org/10.1215/00127094-3129809

Information

Received: 21 August 2013; Revised: 10 October 2014; Published: 1 October 2015
First available in Project Euclid: 5 October 2015

zbMATH: 1352.60007
MathSciNet: MR3405592
Digital Object Identifier: 10.1215/00127094-3129809

Subjects:
Primary: 60B20
Secondary: 15B52

Rights: Copyright © 2015 Duke University Press

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Vol.164 • No. 13 • 1 October 2015
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