Delocalization of eigenvectors of random matrices with independent entries
By Mark Rudelson, Roman Vershynin. 2013
81 citations recorded by the source corpus.
Author(s): Rudelson, Mark; Vershynin, Roman | 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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/997d4fe9afe91b2c21d1377cd531a6fa5167fb18
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In Applied Mathematics
- Konstantin E. Tikhomirov
- Roman Vershynin
- Mark Rudelson
- Galyna V. Livshyts
- Van H. Vu
- Karim Lounici
- Jaouad Mourtada
- Terence Tao
In Computational Theory and Mathematics
- Konstantin E. Tikhomirov
- Roman Vershynin
- Galyna V. Livshyts
- Mark Rudelson
- Joel A. Tropp
- Tamás Sarlós
- Michael W. Mahoney
- Petros Drineas
In Statistics and Probability
- Konstantin E. Tikhomirov
- Roman Vershynin
- Mark Rudelson
- Galyna V. Livshyts
- Van H. Vu
- Jaouad Mourtada
- Nicholas A. Cook
- Terence Tao
Citations in the corpus
- No-gaps delocalization for general random matrices (2015, background): “Proof of Theorem 6.1 on invertibility for general distributions 41 References 44”
- The smallest singular value of inhomogeneous square random matrices (2019, methodology): “We shall follow the scheme developed by Rudelson and Vershynin in [25], the first step of which is to decompose the sphere to the set of compressible and incompressible vectors.”