Geodesic
Random matrices and $K$-theory for exact $C^*$-algebras
Documenta mathematica, Tome 4 (1999), pp. 341-450.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we find asymptotic upper and lower bounds for the spectrum of random operators of the form $$ S^*S=\Big(\sum_{i=1}^ra_i\otimes Y_i^{(n)}\Big)^* \Big(\sum_{i=1}^ra_i\otimes Y_i^{(n)}\Big), $$ where $a_1,\ldots,a_r$ are elements of an exact $C^*$-algebra and $Y_1^{(n)},\ldots,Y_r^{(n)}$ are complex Gaussian random $n\times n$ matrices, with independent entries. Our result can be considered as a generalization of results of Geman (1981) and Silverstein (1985) on the asymptotic behavior of the largest and smallest eigenvalue of a random matrix of Wishart type. The result is used to give new proofs of:
Classification : 46L05, 46L50, 46L35, 46L80, 60F15 
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     author = {Haagerup, U. and Thorbj{\o}rnsen, S.},
     title = {Random matrices and $K$-theory for exact $C^*$-algebras},
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     pages = {341--450},
     publisher = {mathdoc},
     volume = {4},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_1999__4__a8/}
}
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Haagerup, U.; Thorbjørnsen, S. Random matrices and $K$-theory for exact $C^*$-algebras. Documenta mathematica, Tome 4 (1999), pp. 341-450. http://geodesic.mathdoc.fr/item/DOCMA_1999__4__a8/