Résumé : Metric properties of random maps (graphs embedded in surfaces) have been subject to a lot of recent interest. In this talk, I will review a combinatorial approach to these questions, which exploits bijections between maps and some labeled trees. Thanks to an unexpected phenomenon of ``discrete integrability'', it is possible to enumerate exactly maps with two or three points at prescribed distances, and more. I will then discuss probabilistic applications to the study of the Brownian map (obtained as the scaling limit of random planar maps) and of uniform infinite planar maps (obtained as local limits). If time allows, I will also explain the combinatorial origin of discrete integrability, related to the continued fraction expansion of the so-called resolvent of the one-matrix model. Based on joint works with E. Guitter and P. Di Francesco.
|Dernière modification : Friday 13 September 2013||Contact : Cyril.Banderier at lipn.univ-paris13.fr|