Matrix Models vs. Matrix Integrals

Abstract

In a brief review, we discuss interrelations between arbitrary solutions of the loop equations that describe Hermitean one-matrix model and particular (multi-cut) solutions that describe concrete matrix integrals. These latter ones enjoy a series of specific properties and, in particular, are described in terms of Seiberg-Witten-Whitham theory. The simplest example of ordinary integral is considered in detail.

10 pages, contribution to the International Workshop "Classical and Quantum Integrable Systems", Dubna, Russia, 2005

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