The scaling limit of uniform random plane maps, via the Ambjørn-Budd bijection
By Jérémie Bettinelli, Emmanuel Jacob, Grégory Miermont. 2013
92 citations recorded by the source corpus.
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 Ambjorn and Budd allows to derive this result by a direct coupling with a uniform random quadrangulation with n faces.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/85272f1988556484d8d7e263837a4885b67d7f08
How researchers see this paper
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In Geometry and Topology
- Nicolas Curien
- C. Abraham
- Jean-François Le Gall
- Grégory Miermont
- Jérémie Bettinelli
- Guillaume Chapuy
- Rémi Rhodes
- Vincent Vargas
In Mathematical Physics
- Nicolas Curien
- Jean-François Le Gall
- C. Abraham
- Grégory Miermont
- Jérémie Bettinelli
- Igor Kortchemski
- R. Stephenson
- Svante Janson
Citations in the corpus
- Random geometry on the sphere (2014, background): “Similarly, analogs of (1) hold for general planar maps with a fixed number of edges [11] or for bipartite planar maps with a fixed number of edges [1].”
- The hull process of the Brownian plane (2014, background): “A fundamental object is the random compact metric space known as the Brownian map, which has been proved to be the universal scaling limit of several important classes of random planar maps conditioned to have a large size (see in particular [1, 3, 6, 23, 30]).”
- Rescaled bipartite planar maps converge to the Brownian map (2013, background): “Notice that similar arguments appear in [3], Proposition 4.”