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  1. Home > Articles & Issues >
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  3. An invariance princi ...
Conference paper

An invariance principle for random planar maps

Grégory Miermont ORCID (1)
(1) Laboratoire de Mathématiques d'Orsay
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May 10, 2017
Published on
December 31, 2005
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March 31, 2025
Volume 0
DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities
Proceedings
DOI
10.46298/dmtcs.3505
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https://about.hal.science/hal-authorisation-v1
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An invariance principle for random planar maps

Grégory Miermont ORCID (1)
(1) Laboratoire de Mathématiques d'Orsay
Abstract
We show a new invariance principle for the radius and other functionals of a class of conditioned `Boltzmann-Gibbs'-distributed random planar maps. It improves over the more restrictive case of bipartite maps that was discussed in Marckert and Miermont (2006). As in the latter paper, we make use of a bijection between planar maps and a class of labelled multitype trees, due to Bouttier et al. (2004). We also rely on an invariance principle for multitype spatial Galton-Watson trees, which is proved in a companion paper.
Keywords
  • [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • Random planar map
  • invariance principle
  • multitype spatial Galton-Watson tree
  • Brownian snake
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