Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

The two uniform infinite quadrangulations of the plane have the same law

Laurent Ménard

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We prove that the uniform infinite random quadrangulations defined respectively by Chassaing–Durhuus and Krikun have the same distribution.


On démontre que les quadrangulations aléatoires infinies uniformes définies respectivement par Chassaing–Durhuus et par Krikun ont la même loi.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 46, Number 1 (2010), 190-208.

First available in Project Euclid: 1 March 2010

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Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 05C30: Enumeration in graph theory

Random map Random tree Schaeffer’s bijection Uniform infinite planar quadrangulation Uniform infinite planar tree


Ménard, Laurent. The two uniform infinite quadrangulations of the plane have the same law. Ann. Inst. H. Poincaré Probab. Statist. 46 (2010), no. 1, 190--208. doi:10.1214/09-AIHP313.

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