Matrix Models as Integrable Systems

Abstract

The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Determinantal formulas, relation to conformal field models and the theory of Generalized Kontsevich model are discussed in some detail. Attention is also paid to the group-theoretical interpretation of $τ$-functions which allows to go beyond the restricted set of the (multicomponent) KP and Toda integrable hierarchies.

60 pages, LaTeX. Presented at Banff Conference, Banff, Canada, 15-23 August 1994.