Displaying similar documents to “Universality in the random matrix spectra in the regime of weak non-hermiticity”

Universality for certain hermitian Wigner matrices under weak moment conditions

Kurt Johansson (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We study the universality of the local eigenvalue statistics of Gaussian divisible Hermitian Wigner matrices. These random matrices are obtained by adding an independent GUE matrix to an Hermitian random matrix with independent elements, a Wigner matrix. We prove that Tracy–Widom universality holds at the edge in this class of random matrices under the optimal moment condition that there is a uniform bound on the fourth moment of the matrix elements. Furthermore, we show that universality...

Central limit theorems for eigenvalues of deformations of Wigner matrices

M. Capitaine, C. Donati-Martin, D. Féral (2012)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper, we study the fluctuations of the extreme eigenvalues of a spiked finite rank deformation of a Hermitian (resp. symmetric) Wigner matrix when these eigenvalues separate from the bulk. We exhibit quite general situations that will give rise to universality or non-universality of the fluctuations, according to the delocalization or localization of the eigenvectors of the perturbation. Dealing with the particular case of a spike with multiplicity one, we also establish a necessary...

Central limit theorems for eigenvalues in a spiked population model

Zhidong Bai, Jian-Feng Yao (2008)

Annales de l'I.H.P. Probabilités et statistiques

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In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with empirical findings on various data sets. The question is to quantify the effect of the perturbation caused by the spike eigenvalues. A recent work by Baik and Silverstein establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalues when the population...

Spectral properties of large random matrices with independent entries

P. Dueck, S. O'Rourke, D. Renfrew, A. Soshnikov (2011)

Banach Center Publications

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We consider large Wigner random matrices and related ensembles of real symmetric and Hermitian random matrices. Our results are related to the local spectral properties of these ensembles.