Jérémie Bouttier: The two-point function of block-weighted quadrangulations (a challenge in analytic combinatorics)

par Jérémie Bouttier (Sorbonne Université)

jeudi 2 avr. 2026, 11:00 → 12:00 Europe/Paris

Salle Pierre Grisvard (IHP - Bâtiment Borel)

Models of block-weighted random planar maps have recently been introduced and studied by Zéphyr Salvy and William Fleurat, who showed that they display an interesting phase transition, which has been related to Liouville quantum duality by Bertrand Duplantier and Emmanuel Guitter. In this talk, I will discuss a specific instance of such model, namely that of quadrangulations weighted according to their number of simple blocks. Building on results from a 2010 paper on the ``geometry of minbus'', we obtain an exact expression for the two-point function, that is the generating function of block-weighted quadrangulations with two points at a controlled distance. A caveat is however that our result involves a bivariate generating function, which makes the asymptotic analysis harder. The Flajolet seminar is certainly the best place to tell how we faced this challenge. Based on work under completion with Emmanuel Guitter and Hugo Manet.