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Zbl 1120.46051
Collins, Beno{\^\i}t; Śniady, Piotr
(1065.60023)
New scaling of Itzykson-Zuber integrals. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 43, No. 2, 139-146 (2007). ISSN 0246-0203

Summary: We study asymptotics of the Itzykson-Zuber integrals in the scaling when one of the matrices has a small rank compared to the full rank. We show that the result is basically the same as in the case when one of the matrices has a fixed rank. In this way we extend the recent results of {\it A. Guionnet} and {\it M. Ma{\"\i}da} [J. Funct. Anal. 222, No.~2, 435--490 (2005; Zbl 1065.60023)] who showed that for the fixed rank scaling, the Itzykson-Zuber integral is given in terms of Voiculescu's $R$-transform of the full rank matrix.

MSC 2000:: *46L54 Free probability and free operator algebras
15A52 Random matrices

Keywords: Itzykson-Zuber integral; $R$-transform

Citations: Zbl 1065.60023

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