Random matrices and -theory for exact -algebras
U. Haagerup
S. Thorbjørnsen
![Random matrices and $K$-theory for exact $C^*$-algebras cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-dm-volume-4.png&w=3840&q=90)
Abstract
In this paper we find asymptotic upper and lower bounds for the spectrum of random operators of the form
where are elements of an exact -algebra and are complex Gaussian random 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:
Cite this article
U. Haagerup, S. Thorbjørnsen, Random matrices and -theory for exact -algebras. Doc. Math. 4 (1999), pp. 341–450
DOI 10.4171/DM/63