The matrix model for dessins d'enfants

@article{Ambjrn2014TheMM,
  title={The matrix model for dessins d'enfants},
  author={J. Ambj{\o}rn and L. Chekhov},
  journal={arXiv: Algebraic Geometry},
  year={2014}
}
We present the matrix models that are the generating functions for branched covers of the complex projective line ramified over $0$, $1$, and $\infty$ (Grotendieck's dessins d'enfants) of fixed genus, degree, and the ramification profile at infinity. For general ramifications at other points, the model is the two-logarithm matrix model with the external field studied previously by one of the authors (L.Ch.) and K.Palamarchuk. It lies in the class of the generalised Kontsevich models (GKM) thus… Expand
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