REVIEW 2 cited by
The Brownian map is the scaling limit of uniform random plane quadrangulations
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
We prove that uniform random quadrangulations of the sphere with $n$ faces, endowed with the usual graph distance and renormalized by $n^{-1/4}$, converge as $n\to\infty$ in distribution for the Gromov-Hausdorff topology to a limiting metric space. We validate a conjecture by Le Gall, by showing that the limit is (up to a scale constant) the so-called {\em Brownian map}, which was introduced by Marckert & Mokkadem and Le Gall as the most natural candidate for the scaling limit of many models of random plane maps. The proof relies strongly on the concept of {\em geodesic stars} in the map, which are configurations made of several geodesics that only share a common endpoint and do not meet elsewhere.
Forward citations
Cited by 2 Pith papers
-
Random walk reflected off of infinity, with applications to uniform spanning forests and supercritical Liouville quantum gravity
A random walk that reflects off the boundary at infinity yields new algorithmic constructions of the free uniform spanning forest and a conjectural embedding framework for supercritical Liouville quantum gravity.
-
Random surfaces and Liouville quantum gravity
An expository overview of the definition of Liouville quantum gravity surfaces, the three senses in which random planar maps converge to them, and the major open problems.
Discussion (0). Continue with ORCID to comment.