Les deux quadrangulations infinies uniformes ont m\^eme loi

TL;DR

This paper proves that two different models of uniform infinite random quadrangulations are statistically identical in distribution, unifying previous separate constructions.

Contribution

It establishes the equivalence in distribution of two independently introduced models of uniform infinite quadrangulations.

Findings

Both models have the same probability distribution.

The result unifies different approaches to infinite quadrangulations.

It simplifies the understanding of the structure of infinite random quadrangulations.

Abstract

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