Can I read Non universality of fluctuations of outlier eigenvectors for block diagonal deformations of Wigner matrices on EtoBox?

Non universality of fluctuations of outlier eigenvectors for block diagonal deformations of Wigner matrices by Capitaine, Mireille; Donati-Martin, Catherine is a scholarly article available to read on EtoBox.

What is Non universality of fluctuations of outlier eigenvectors for block diagonal deformations of Wigner matrices about?

In this paper, we investigate the fluctuations of a unit eigenvector associated to an outlier in the spectrum of a spiked $N\times N$ complex Deformed Wigner matrix $M_N$: $M_N =W_N/\sqrt{N} + A_N$ where $W_N$ is an $N \times N$ Hermitian Wigner matrix whose entries have a law $\mu$ satisfying a Poincar\'e inequality and the matrix $A_N$ is a block diagonal matrix, with an eigenvalue $\theta$ of multiplicity one, generating an outlier in the spectrum of $M_N$. We prove that the fluctuations of the norm of the projection of a unit eigenvector corresponding to the outlier of $M_N$ onto a unit eigenvector corresponding to $\theta$ are not universal.

Author

Capitaine, Mireille; Donati-Martin, Catherine

Published

2018

Language

EN