The scaling limit of uniform random plane maps, via the Ambjørn-Budd bijection

Jérémie Bettinelli (1) , Emmanuel Jacob (2) , Grégory Miermont (2)

1 IECL - Institut Élie Cartan de Lorraine
2 ENS de Lyon - École normale supérieure de Lyon

We prove that a uniform rooted plane map with n edges converges in distribution after a suitable normalization to the Brownian map for the Gromov-Hausdorff topology. A recent bijection due to Ambjørn and Budd allows to derive this result by a direct coupling with a uniform random quadrangulation with n faces.

Mots clés: Gromov-Hausdorff topology; Brownian map; random maps; bijections; random metric spaces; scaling limits

Domaines: Probabilités [math.PR]

Jérémie Bettinelli, Emmanuel Jacob, Grégory Miermont. The scaling limit of uniform random plane maps, via the Ambjørn-Budd bijection. Electronic Journal of Probability, 2014, 19 (73), pp.1--16. ⟨10.1214/EJP.v19-3213⟩. ⟨hal-00921179⟩