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

Jérémie L Bettinelli (Institut Élie Cartan de Lorraine)
Emmanuel Jacob (École Normale Supérieure de Lyon)
Grégory Miermont (École Normale Supérieure de Lyon)


We prove that a uniform rooted plane map with n edges converges in distribution after asuitable 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.

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Pages: 1-16

Publication Date: August 19, 2014

DOI: 10.1214/EJP.v19-3213


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