21:35
published on March 31, 2025
Pattern avoiding 3-permutations and triangle bases
By Juliette Schabanel
Vertex degrees in planar maps
Appears in 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
