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math.PR2021
Random generation and scaling limits of fixed genus factorizations into transpositions
Valentin Féray, Baptiste Louf, Paul Thévenin
We study the asymptotic behaviour of random factorizations of the -cycle into transpositions of fixed genus . They have a geometric interpretation as branched covers of the…
math.PR2021
Short cycles in high genus unicellular maps
Svante Janson, Baptiste Louf
We study large uniform random maps with one face whose genus grows linearly with the number of edges, which are a model of discrete hyperbolic geometry. In previous works, several…
math.PR2020
Local limits of bipartite maps with prescribed face degrees in high genus
Thomas Budzinski, Baptiste Louf
We study the local limits of uniform high genus bipartite maps with prescribed face degrees. We prove the convergence towards a family of infinite maps of the plane, the q-IBPMs, w…