Bernoulli

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

Quadrangulations with no pendant vertices

Johel Beltran and Jean-François Le Gall

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 27 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1377612847

Digital Object Identifier
doi:10.3150/12-BEJSP13

Mathematical Reviews number (MathSciNet)
MR3102547

Zentralblatt MATH identifier
1286.60003

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

Citation

Beltran, Johel; Le Gall, Jean-François. Quadrangulations with no pendant vertices. Bernoulli 19 (2013), no. 4, 1150--1175. doi:10.3150/12-BEJSP13. https://projecteuclid.org/euclid.bj/1377612847


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