# Random generation and scaling limits of fixed genus factorizations into transpositions

@inproceedings{Feray2021RandomGA, title={Random generation and scaling limits of fixed genus factorizations into transpositions}, author={Valentin F'eray and Baptiste Louf and Paul Th'evenin}, year={2021} }

We study the asymptotic behaviour of random factorizations of the n-cycle into transpositions of fixed genus g > 0. They have a geometric interpretation as branched covers of the sphere and their enumeration as Hurwitz numbers was extensively studied in algebraic combinatorics and enumerative geometry. On the probabilistic side, several models and properties of permutation factorizations were studied in previous works, in particular minimal factorizations of cycles into transpositions (which… Expand

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