Publication : t05/047

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

Eynard B. (CEA, DSM, SPhT (Service de Physique Thorique), F-91191 Gif-sur-Yvette, FRANCE)
Abstract:
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.
Année de publication : 2005
Thse d'habilitation
Pages : 86 pp.
Soutenance de thse : Universit Paris VII ; 2005-09-15
Preprint : arXiv:math-ph/0504034
Langue : Français
Editeurs : Brzin E.

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