The scaling limit of uniform random plane maps, via the Ambjrn-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 Ambjrn and Budd allows to derive this result by a direct coupling with a uniform random quadrangulation with n faces.
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