For WLZZ two-matrix models, integration contours describe only a finite-N subspace of Ward identity solutions, and the full solution space is recovered only in the N-to-infinity limit.
Matrix Models vs. Matrix Integrals
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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.
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Phases in WLZZ Matrix Models
For WLZZ two-matrix models, integration contours describe only a finite-N subspace of Ward identity solutions, and the full solution space is recovered only in the N-to-infinity limit.