Direct proofs of determinantal formulas for connected k-point functions and KP integrability are given for hermitian matrix models, plus duality for some models.
Grothendieck's Dessins d'Enfants in a Web of Dualities
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this paper we show that counting Grothendieck's dessins d'enfants is universal in the sense that some other enumerative problems are either special cases or directly related to it. Such results provide concrete examples that support a proposal made in the paper to study various dualities from the point of view of group actions on the moduli space of theories. Connections to differential equations of hypergeometric type can be made transparent from this approach, suggesting a connection to mirror symmetry.
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Spectral curve for Eynard-Orantin recursions on dessins d'enfants is related to Narayana numbers.
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On determinantal formulas for hermitian random matrices
Direct proofs of determinantal formulas for connected k-point functions and KP integrability are given for hermitian matrix models, plus duality for some models.
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Grothendieck's Dessins d'Enfants in a Web of Dualities. II
Spectral curve for Eynard-Orantin recursions on dessins d'enfants is related to Narayana numbers.