2014/03/31 by Joel Bun, Jo el Bun, Jean‐Philippe Bouchaud +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Brownian motion #Eigenvalues and eigenvectors #Formalism (music) #Instanton #Mathematical functions and polynomials #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Symplectic geometry #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevlett.113.070201
published as Phys. Rev. Lett. 113, 070201 (2014) · 5 pages, 1 figure
openalex publication_date 2014/08/14 · arxiv created 2014/09/05 · arxiv updated 2014/09/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.