On delocalization of eigenvectors of random non-Hermitian matrices

@article{Lytova2018OnDO,
  title={On delocalization of eigenvectors of random non-Hermitian matrices},
  author={Anna Lytova and Konstantin E. Tikhomirov},
  journal={Probability Theory and Related Fields},
  year={2018},
  volume={177},
  pages={465-524}
}
We study delocalization of null vectors and eigenvectors of random matrices with i.i.d entries. Let A be an $$n\times n$$ n × n random matrix with i.i.d real subgaussian entries of zero mean and unit variance. We show that with probability at least $$1-e^{-\log ^{2} n}$$ 1 - e - log 2 n $$\begin{aligned} \min \limits _{I\subset [n],\,|I|= m}\Vert \mathbf{{v}}_I\Vert \ge \frac{m^{3/2}}{n^{3/2}\log ^Cn}\Vert \mathbf{{v}}\Vert \end{aligned}$$ min I ⊂ [ n ] , | I | = m ‖ v I ‖ ≥ m 3 / 2 n 3 / 2 log… Expand
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