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.
Generating series for GUE correlators
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abstract
We extend to the Toda lattice hierarchy the approach of [3, 4] to computation of logarithmic derivatives of tau-functions in terms of the so-called matrix resolvents of the corresponding differ- ence Lax operator. As a particular application we obtain explicit generating series for connected GUE correlators. On this basis an efficient recursive procedure for computing the correlators in full genera is developed.
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Summing non-perturbative contributions in the gravitational path integral, extended via matrix integral saddles including one- and two-eigenvalue instantons, resolves negativity of bulk entropies in two-sided black holes.
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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.