Critical multi-type Galton- Watson trees conditioned to be large

Romain Abraham (1) , Jean-François Delmas (2) , Hongsong Guo (3)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 BNU - Beijing Normal University

Under minimal condition, we prove the local convergence of a critical multi-type Galton-Watson tree conditioned on having a large total progeny by types towards a multi-type Kesten's tree. We obtain the result by generalizing Neveu's strong ratio limit theorem for aperiodic random walks on Z^d .

Domaines: Probabilités [math.PR]

Romain Abraham, Jean-François Delmas, Hongsong Guo. Critical multi-type Galton- Watson trees conditioned to be large. Journal of Theoretical Probability, 2018, 31, pp.757-788. ⟨10.1007/s10959-016-0739-8⟩. ⟨hal-01224696v2⟩