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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Abstract

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

Résumé

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

Article information

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

Dates
First available in Project Euclid: 1 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1267454114

Digital Object Identifier
doi:10.1214/09-AIHP313

Mathematical Reviews number (MathSciNet)
MR2641776

Zentralblatt MATH identifier
1201.60009

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

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

Citation

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. https://projecteuclid.org/euclid.aihp/1267454114


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