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- W2934566931 abstract "We consider matrices formed by a random $Ntimes N$ matrix drawn from the Gaussian Orthogonal Ensemble (or Gaussian Unitary Ensemble) plus a rank-one perturbation of strength $theta$, and focus on the largest eigenvalue, $x$, and the component, $u$, of the corresponding eigenvector in the direction associated to the rank-one perturbation. We obtain the large deviation principle governing the atypical joint fluctuations of $x$ and $u$. Interestingly, for $theta>1$, in large deviations characterized by a small value of $u$, i.e. $u<1-1/theta$, the second-largest eigenvalue pops out from the Wigner semi-circle and the associated eigenvector orients in the direction corresponding to the rank-one perturbation. We generalize these results to the Wishart Ensemble, and we extend them to the first $n$ eigenvalues and the associated eigenvectors." @default.
- W2934566931 created "2019-04-11" @default.
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- W2934566931 date "2020-09-30" @default.
- W2934566931 modified "2023-10-10" @default.
- W2934566931 title "Large deviations for the largest eigenvalues and eigenvectors of spiked random matrices" @default.
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