Instanton Approach to Large $N$ Harish-Chandra-Itzykson-Zuber Integrals

Joel Bun 1, 2, 3 Jean-Philippe Bouchaud 1 Satya N. Majumdar 2 Marc Potters 1

Physical Review Letters, American Physical Society, 2014, 113, pp.070201

We reconsider the large $N$ asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary case. Our method is easily generalized to the orthogonal and symplectic ensembles. We obtain an explicit solution of Matytsin's equations in the case of Wigner matrices, as well as a general expansion method in the dilute limit, when the spectrum of eigenvalues spreads over very wide regions.

  • 1. Science et Finance
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 3. Pole Univ Leonard de Vinci