Second and Third Order Observables of the Two-Matrix Model

Abstract

In this paper we complement our recent result on the explicit formula for the planar limit of the free energy of the two-matrix model by computing the second and third order observables of the model in terms of canonical structures of the underlying genus g spectral curve. In particular we provide explicit formulas for any three-loop correlator of the model. Some explicit examples are worked out.

22 pages, v2 with added references and minor corrections

References in corpus (18)

• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Conformal maps and dispersionless integrable hierarchies
• Integrable Structure of the Dirichlet Boundary Problem in Two Dimensions
• Duality, Biorthogonal Polynomials and Multi-Matrix Models
• Large N expansion of the 2-matrix model
• Differential systems for biorthogonal polynomials appearing in 2-matrix models and the associated Riemann-Hilbert problem
• Complex Curve of the Two Matrix Model and its Tau-function
• Master loop equations, free energy and correlations for the chain of matrices
• Large scale correlations in normal and general non-Hermitian matrix ensembles
• Free Energy of the Two-Matrix Model/dToda Tau-Function
• Bilinear semi-classical moment functionals and their integral representation
• Dispersionless limit of Hirota equations in some problems of complex analysis
• Mixed Correlation Functions of the Two-Matrix Model
• Large N expansion of the 2-matrix model, multicut case
• Free bosons and tau-functions for compact Riemann surfaces and closed smooth Jordan curves I. Current correlation functions
• Tau-function on Hurwitz spaces
• On G-function of Frobenius manifolds related to Hurwitz spaces
• Duality of spectral curves arising in two-matrix models

Cited by in corpus (7)

• Free energy topological expansion for the 2-matrix model
• Matrix eigenvalue model: Feynman graph technique for all genera
• Genus one contribution to free energy in hermitian two-matrix model
• Matrix models with hard walls: Geometry and solutions
• The 2-matrix model, biorthogonal polynomials, Riemann-Hilbert problem, and algebraic geometry
• Two-matrix model with semiclassical potentials and extended Whitham hierarchy
• Formal matrix integrals and combinatorics of maps