A view from infinity of the uniform infinite planar quadrangulation
By Nicolas Curien, Laurent M'enard, Grégory Miermont. 2012
75 citations recorded by the source corpus.
We introduce a new construction of the Uniform Infinite Planar Quadrangulation (UIPQ). Our approach is based on an extension of the Cori-Vauquelin-Schaeffer mapping in the context of infinite trees, in the spirit of previous work. However, we release the positivity constraint on the labels of trees which was imposed in these references, so that our construction is technically much simpler. This approach allows us to prove the conjectures of Krikun pertaining to the "geometry at infinity" of the UIPQ, and to derive new results about the UIPQ, among which a fine study of infinite geodesics.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5b065358d53e55954da7d1798a30078b90a323be
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Hyperbolic and Parabolic Unimodular Random Maps (2016, unknown): “08 69 3v 2 [ m at h. PR ] 2 1 M ar 2 01 8”
- Planar stochastic hyperbolic triangulations (2016, methodology): “The UIPT and its quadrangular analog the UIPQ have received a lot of attention in recent years [4, 12, 22, 27, 31] partially motivated by the connections with the physics theory of 2dimensional quantum gravity, the Gaussian free field [19] and the Brownian map [20, 30, 34].”