Bun J, Bouchaud JP, Majumdar SN, Potters M. Instanton approach to large N Harish-Chandra-Itzykson-Zuber integrals.
Phys Rev Lett 2014;
113:070201. [PMID:
25170689 DOI:
10.1103/physrevlett.113.070201]
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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.
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