New scaling of Itzykson-Zuber integrals

Details New scaling of Itzykson-Zuber integrals New scaling of Itzykson-Zuber integrals

2005-05-30

arxiv.org/abs/math/0505664v1

Ann. Inst. H. Poincare Probab. Statist. 43 (2007) no. 2, 139--146

Mathematics

Probability

Scientific paper

10.1016/j.anihpb.2005.12.003

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 Guionnet and Maida who showed that for a latter scaling the Itzykson-Zuber integral is given in terms of the Voiculescu's R-transform of the full rank matrix.

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