Apparaît dans les collections : Random trees and maps: probabilistic and combinatorial aspects / Arbres et cartes aléatoires : aspects probabilistes et combinatoires, Exposés de recherche
We consider the family of rooted planar maps $M_\Omega$ where the vertex degrees belong to a (possibly infinite) set of positive integers $\Omega$. Using a classical bijection with mobiles and some refined analytic tools in order to deal with the systems of equations that arise, we recover a universal asymptotic behavior of planar maps. Furthermore we establish that the number of vertices of a given degree satisfies a multi (or even infinitely)-dimensional central limit theorem. We also discuss some possible extension to maps of higher genus. This is joint work with Gwendal Collet and Lukas Klausner
De Colin Guillarmou
De Bernhard Keller
