title: Instanton approach to large N Harish-Chandra-Itzykson-Zuber integrals.
abstract: 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.
authors.affiliation: Capital Fund Management, 23-25, rue de l'Université, 75007 Paris, France and CNRS, LPTMS, Batiment 100, Université d'Orsay, 91405 Orsay Cedex, France and DeVinci Finance Lab, Pôle Universitaire Léonard de Vinci, 92916 Paris La Défense, France.
authors.forename: J
authors.initials: J
authors.lastname: Bun
authors.affiliation: Capital Fund Management, 23-25, rue de l'Université, 75007 Paris, France.
authors.forename: J P
authors.initials: JP
authors.lastname: Bouchaud
authors.affiliation: CNRS, LPTMS, Batiment 100, Université d'Orsay, 91405 Orsay Cedex, France.
authors.forename: S N
authors.initials: SN
authors.lastname: Majumdar
authors.affiliation: Capital Fund Management, 23-25, rue de l'Université, 75007 Paris, France.
authors.forename: M
authors.initials: M
authors.lastname: Potters