A two-matrix model is introduced whose 1/N expansion yields higher-genus Fuss-Catalan numbers for arbitrary p, together with sum rules and an explicit formula extending the Harer-Zagier result.
Unification of All String Models with $c<1$
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abstract
A 1-matrix model is proposed, which nicely interpolates between double-scaling continuum limits of all multimatrix models. The interpolating partition function is always a KP $\tau $-function and always obeys ${\cal L}_{-1}$-constraint and string equation. Therefore this model can be considered as a natural unification of all models of 2d-gravity (string models) with $c\leq 1.$
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A Matrix Model for Higher-Genus Fuss--Catalan Numbers
A two-matrix model is introduced whose 1/N expansion yields higher-genus Fuss-Catalan numbers for arbitrary p, together with sum rules and an explicit formula extending the Harer-Zagier result.