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

J. Bun, J. P. Bouchaud, S. N. Majumdar, and M. Potters
Phys. Rev. Lett. 113, 070201 – Published 14 August 2014

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.

  • Figure
  • Received 15 April 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.070201

© 2014 American Physical Society

Authors & Affiliations

J. Bun1,2,3,*, J. P. Bouchaud1, S. N. Majumdar2, and M. Potters1

  • 1Capital Fund Management, 23–25, rue de l’Université, 75007 Paris, France
  • 2CNRS, LPTMS, Batiment 100, Université d’Orsay, 91405 Orsay Cedex, France
  • 3DeVinci Finance Lab, Pôle Universitaire Léonard de Vinci, 92916 Paris La Défense, France

  • *joel.bun@u-psud.fr

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Issue

Vol. 113, Iss. 7 — 15 August 2014

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