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.
Gromov-Witten theory, Hurwitz numbers, and Matrix models, I
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abstract
The main goal of the paper is to present a new approach via Hurwitz numbers to Kontsevich's combinatorial/matrix model for the intersection theory of the moduli space of curves. A secondary goal is to present an exposition of the circle of ideas involved: Hurwitz numbers, Gromov-Witten theory of the projective line, matrix integrals, and the theory of random trees. Further topics will be treated in a sequel.
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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.