Delocalization of eigenvectors of random matrices with independent entries
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Delocalization of eigenvectors of random matrices with independent entries

  • Author(s): Rudelson, M
  • Vershynin, R
  • et al.
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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