Quadrangulations with no pendant vertices

Abstract

We prove that the metric space associated with a uniformly distributed planar quadrangulation with n faces and no pendant vertices converges modulo a suitable rescaling to the Brownian map. This is a first step towards the extension of recent convergence results for random planar maps to the case of graphs satisfying local constraints.

Published in at http://dx.doi.org/10.3150/12-BEJSP13 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (3)

• Uniqueness and universality of the Brownian map
• The topological structure of scaling limits of large planar maps
• Scaling limits of random trees and planar maps

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• Scaling limits of random bipartite planar maps with a prescribed degree sequence
• The scaling limit of random simple triangulations and random simple quadrangulations
• Stability of geodesics in the Brownian map
• Convergence of odd-angulations via symmetrization of labeled trees
• Compact Brownian surfaces I. Brownian disks
• The Brownian plane with minimal neck baby universe
• Random Lévy Looptrees and Lévy Maps