• Bernoulli
  • Volume 19, Number 4 (2013), 1150-1175.

Quadrangulations with no pendant vertices

Johel Beltran and Jean-François Le Gall

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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.

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Bernoulli, Volume 19, Number 4 (2013), 1150-1175.

First available in Project Euclid: 27 August 2013

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Brownian map Gromov–Hausdorff convergence pendant vertex quadrangulation well-labeled tree


Beltran, Johel; Le Gall, Jean-François. Quadrangulations with no pendant vertices. Bernoulli 19 (2013), no. 4, 1150--1175. doi:10.3150/12-BEJSP13.

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