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

Abstract

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.

References in corpus (3)

• The topological structure of scaling limits of large planar maps
• The three-point function of planar quadrangulations
• On the two-point function of general planar maps and hypermaps

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