REVIEW 3 cited by
Local structure of random 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
read the original abstract
This paper is an adaptation of a method used in \cite{K} to the model of random quadrangulations. We prove local weak convergence of uniform measures on quadrangulations and show that the local growth of quadrangulation is governed by certain critical time-reversed branching process and the rescaled profile converges to the reversed continuous-state branching process. As an intermediate result we derieve a biparametric generating function for certain class of quadrangulations with boundary.
Forward citations
Cited by 3 Pith papers
-
Local convergence of random planar graphs
Uniform connected planar graphs have a quenched local limit, a new infinite random graph called the uniform infinite planar graph (UIPG).
-
Characterisation of Markov property on planar maps
The only rerooting-invariant Markovian random quadrangulations are Boltzmann maps, and every submap that induces a Markovian decomposition is a 'stopping map,' a class strictly larger than peeling explorations.
-
First-passage percolation in random planar maps and Tutte's bijection
FPP distance in random quadrangulations and planar maps scales asymptotically as a constant times graph distance; Tutte bijection preserves this equivalence at large scales.
Discussion (0). Continue with ORCID to comment.