The 2-matrix model, biorthogonal polynomials, Riemann-Hilbert problem, and algebraic geometry

Details The 2-matrix model, biorthogonal polynomials, Riemann-Hilbert problem, and algebraic geometry The 2-matrix model, biorthogonal polynomials, Riemann-Hilbert problem, and algebraic geometry

2005-04-08

arxiv.org/abs/math-ph/0504034v1

Physics

Mathematical Physics

in french, latex, 80 pages

Scientific paper

This preprint is the introduction of my habilitation thesis for Paris7 university. It is a sumary of a collection of works on the 2 matrix model. In an introduction, 3 different and unequivalent definitions of matrix models are given (convergent model, model with fixed filling fractions on contours, and formal model). Then, a sumary of properties of differential systems satisfied by biorthogonal polynomials, in particular spectral duality and Riemann-Hilbert problem. Then, a section on loop equations and algebraic geometry formulation of the large N expansion. Then, a conjecture for the asymptotics of biorthogonal polynomials.

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