2014/01/12 by Alice Guionnet, Guionnet, Alice, Jonathan Novak +1 · 1 citation
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1401.2703
openalex publication_date 2014/01/12 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We prove the existence of a 1/N expansion in unitary multimatrix models which\nare Gibbs perturbations of the Haar measure, and express the expansion\ncoefficients recursively in terms of the unique solution of a noncommutative\ninitial value problem. The recursion obtained is closely related to the\n"topological recursion" which underlies the asymptotics of many random matrix\nensembles and appears in diverse enumerative geometry problems, but has not\npreviously appeared in the context of random unitary matrices. Our approach\nconsists of two main ingredients: an asymptotic study of the Schwinger-Dyson\nlattice over noncommutative Laurent polynomials, and uniform control on the\ncumulants of Gibbs measures on product unitary groups. The required cumulant\nbounds are obtained by concentration of measure arguments.\n