Electronic Journal of Probability

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

Jérémie Bettinelli, Emmanuel Jacob, and Grégory Miermont

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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.

Article information

Electron. J. Probab., Volume 19 (2014), paper no. 74, 16 pp.

Accepted: 19 August 2014
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60C05: Combinatorial probability

random maps scaling limits Brownian map Gromov-Hausdorff topology random metric spaces bijections

This work is licensed under a Creative Commons Attribution 3.0 License.


Bettinelli, Jérémie; Jacob, Emmanuel; Miermont, Grégory. The scaling limit of uniform random plane maps, via the Ambjørn–Budd bijection. Electron. J. Probab. 19 (2014), paper no. 74, 16 pp. doi:10.1214/EJP.v19-3213. https://projecteuclid.org/euclid.ejp/1465065716

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