6 papers
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…
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…
Large expanders in high genus unicellular maps
Baptiste Louf
We study large uniform random maps with one face whose genus grows linearly with the number of edges. They can be seen as a model of discrete hyperbolic geometry. In the past, seve…
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…
Simple formulas for constellations and bipartite maps with prescribed degrees
Baptiste Louf
We obtain simple quadratic recurrence formulas counting bipartite maps on surfaces with prescribed degrees (in particular, -angulations), and constellations. These formulas are…
A new family of bijections for planar maps
Baptiste Louf
We present bijections for the planar cases of two counting formulas on maps that arise from the KP hierarchy (Goulden-Jackson and Carrell-Chapuy formulas), relying on a "cut-and-sl…