Local structure of random quadrangulations
Probability
2007-05-23 v2
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.
Cite
@article{arxiv.math/0512304,
title = {Local structure of random quadrangulations},
author = {Maxim Krikun},
journal= {arXiv preprint arXiv:math/0512304},
year = {2007}
}
Comments
23 pages, 10 figures