Electronic Journal of Probability

Radius and profile of random planar maps with faces of arbitrary degrees

Grégory Miermont and Mathilde Weill

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We prove some asymptotic results for the radius and the profile of large random planar maps with faces of arbitrary degrees. Using a bijection due to Bouttier, Di Francesco & Guitter between rooted planar maps and certain four-type trees with positive labels, we derive our results from a conditional limit theorem for four-type spatial Galton-Watson trees.

Article information

Electron. J. Probab., Volume 13 (2008), paper no. 4, 79-106.

Accepted: 20 January 2008
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 05J30

Random planar map invariance principle multitype spatial Galton-Watson tree Brownian snake

This work is licensed under aCreative Commons Attribution 3.0 License.


Miermont, Grégory; Weill, Mathilde. Radius and profile of random planar maps with faces of arbitrary degrees. Electron. J. Probab. 13 (2008), paper no. 4, 79--106. doi:10.1214/EJP.v13-478. https://projecteuclid.org/euclid.ejp/1464819077

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