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Remarks on 'Coloring Random Triangulation' (1998)

We transform the two-matrix model, studied by P.Di Francesco and al., into a normal one-matrix model by identifying a 'formal' integral used by these authors as a proper integral. We show also, using their method, that the results obtained for the resolvent and the density are not reliable.

On the critical behaviour of hermitean f-matrix models in the double scaling limit with f >= 3 (1999)

Balaska, S. ; Maeder, J. ; Rühl, Werner

An algorithm for the isolation of any singularity of f-matrix models in the double scaling limit is presented. In particular it is proved by construction that only those universality classes exist that are known from 2-matrix models.

The Continuous Series of Critical Points of the Two-Matrix Model at N -> infinity in the Double Scaling Limit (1998)

Balaska, S. ; Maeder, J. ; Rühl, Werner

The critical points of the continuous series are characterized by two complex numbers l_1,l_2 (Re(l_1,l_2)< 0), and a natural number n (n>=3) which enters the string susceptibility constant through gamma = -2/(n-1). The critical potentials are analytic functions with a convergence radius depending on l_1 or l_2. We use the orthogonal polynomial method and solve the Schwinger-Dyson equations with a technique borrowed from conformal field theory.

Perturbative approach to the critical behaviour of two-matrix models in the limit N -> infinity (1997)

Balaska, S ; Maeder, J ; Rühl, Werner

We construct representations of the Heisenberg algebra by pushing the perturbation expansion to high orders.

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