A Survey on the Eigenvalues Local Behavior of Large Complex Correlated Wishart Matrices

Abstract : The aim of this note is to provide a pedagogical survey of the recent works by the authors ( arXiv:1409.7548 and arXiv:1507.06013) concerning the local behavior of the eigenvalues of large complex correlated Wishart matrices at the edges and cusp points of the spectrum: Under quite general conditions, the eigenvalues fluctuations at a soft edge of the limiting spectrum, at the hard edge when it is present, or at a cusp point, are respectively described by mean of the Airy kernel, the Bessel kernel, or the Pearcey kernel. Moreover, the eigenvalues fluctuations at several soft edges are asymptotically independent. In particular, the asymptotic fluctuations of the matrix condition number can be described. Finally, the next order term of the hard edge asymptotics is provided.
Type de document :
Pré-publication, Document de travail
29 pages; 7 figures; to be published in the "Proceedings of the Journées MAS 2014". 2015
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Contributeur : Jamal Najim <>
Soumis le : mercredi 16 septembre 2015 - 14:01:32
Dernière modification le : vendredi 17 février 2017 - 16:15:01
Document(s) archivé(s) le : mardi 29 décembre 2015 - 07:32:05

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  • HAL Id : hal-01199904, version 1
  • ARXIV : 1509.04910

Citation

Walid Hachem, Adrien Hardy, Jamal Najim. A Survey on the Eigenvalues Local Behavior of Large Complex Correlated Wishart Matrices. 29 pages; 7 figures; to be published in the "Proceedings of the Journées MAS 2014". 2015. <hal-01199904>

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