A Survey on the Eigenvalues Local Behavior of Large Complex Correlated Wishart MatricesReportar como inadecuado




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1 LTCI - Laboratoire Traitement et Communication de l-Information 2 LPP - Laboratoire Paul Painlevé 3 LIGM - Laboratoire d-Informatique Gaspard-Monge

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.

Keywords : Bessel kernel Airy kernel Wishart matrices local fluctuations Large random matrices Pearcey kernel





Autor: Walid Hachem - Adrien Hardy - Jamal Najim -

Fuente: https://hal.archives-ouvertes.fr/



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