Local structure of random quadrangulations

Maxim Krikun (1)

1 IECN - Institut Élie Cartan de Nancy

This paper is an adaptation of a method used in math.PR/0311127 to the model of random quadrangulations. We prove local weak convergence of uniform measures on quadrangulations and show that local growth of quadrangulation is governed by certain critical time-reversed branching process. As an intermediate result we calculate a biparametric generating function for certain class of quadrangulations with boundary.

Domaines: Probabilités [math.PR]

Maxim Krikun. Local structure of random quadrangulations. 2005. ⟨hal-00015811v1⟩