New scaling of Itzykson-Zuber integrals
arXiv:math/0505664 · doi:10.1016/j.anihpb.2005.12.003
Abstract
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.
Cited by in corpus (7)
- High-temperature Expansions and Message Passing Algorithms
- Lozenge tilings and Hurwitz numbers
- Canonical moments and random spectral measures
- A Dynamical Mean-Field Theory for Learning in Restricted Boltzmann Machines
- High Temperature Asymptotics of Orthogonal Mean-Field Spin Glasses
- Analysis of Bayesian Inference Algorithms by the Dynamical Functional Approach
- Right large deviation principle for the top eigenvalue of the sum or product of invariant random matrices