Volume 51, October 2015Modélisation Aléatoire et Statistique - Journées MAS 2014
|Page(s)||150 - 174|
|Published online||12 October 2015|
A Survey on the Eigenvalues Local Behavior of Large Complex Correlated Wishart Matrices
1 CNRS LTCI; Télécom
ParisTech, 46 rue
Paris Cedex 13,
2 Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, 10044 Stockholm, Sweden.
3 CNRS LIGM; Université Paris-Est, Cité Descartes, 5 Boulevard Descartes, Champs sur Marne, 77 454 Marne la Vallée Cedex 2, France.
The aim of this note is to provide a pedagogical survey of the recent works [30, 31] 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.
© EDP Sciences, SMAI 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.