Local structure of random quadrangulations

Details Local structure of random quadrangulations Local structure of random quadrangulations

2005-12-14

arxiv.org/abs/math/0512304v2

Mathematics

Probability

23 pages, 10 figures

Scientific paper

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.

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