An invariance principle for random planar maps

Grégory Miermont

doi:10.46298/dmtcs.3505

Grégory Miermont - An invariance principle for random planar maps

dmtcs:3505 - Discrete Mathematics & Theoretical Computer Science, January 1, 2006, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities - https://doi.org/10.46298/dmtcs.3505

An invariance principle for random planar mapsConference paper

Authors: Grégory Miermont ¹

1 Laboratoire de Mathématiques d'Orsay

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.

https://doi.org/10.46298/dmtcs.3505

Source: HAL:hal-01184709v1

Volume: DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities

Section: Proceedings

Published on: January 1, 2006

Imported on: May 10, 2017

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], [en] Random planar map, invariance principle, multitype spatial Galton-Watson tree, Brownian snake

Bibliographic References

19 Documents citing this article

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Olivier Bernardi;Nicolas Curien;Grégory Miermont, 2018, A Boltzmann Approach to Percolation on Random Triangulations, Canadian Journal of Mathematics, 71, 1, pp. 1-43, 10.4153/cjm-2018-009-x, https://doi.org/10.4153/cjm-2018-009-x.

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Jérémie Bettinelli;Emmanuel Jacob;Grégory Miermont, 2014, The scaling limit of uniform random plane maps, via the Ambjørn–Budd bijection, Electronic Journal of Probability, 19, none, 10.1214/ejp.v19-3213, https://doi.org/10.1214/ejp.v19-3213.

Grégory Miermont, 2013, The Brownian map is the scaling limit of uniform random plane quadrangulations, Acta Mathematica, 210, 2, pp. 319-401, 10.1007/s11511-013-0096-8, https://doi.org/10.1007/s11511-013-0096-8.

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Nicolas Curien;Jean-François Le Gall;Grégory Miermont, 2013, The Brownian cactus I. Scaling limits of discrete cactuses, Annales de l Institut Henri Poincaré Probabilités et Statistiques, 49, 2, 10.1214/11-aihp460, https://doi.org/10.1214/11-aihp460.

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Grégory Miermont, 2009, Random Maps and Their Scaling Limits, Progress in probability, pp. 197-224, 10.1007/978-3-0346-0030-9_7.

Grégory Miermont, 2008, Invariance principles for spatial multitype Galton–Watson trees, Annales de l Institut Henri Poincaré Probabilités et Statistiques, 44, 6, 10.1214/07-aihp157, https://doi.org/10.1214/07-aihp157.

Jean-François Le Gall, 2008, The continuous limit of large random planar maps, Discrete Mathematics & Theoretical Computer Science, DMTCS Proceedings vol. AI,..., Proceedings, 10.46298/dmtcs.3554, https://doi.org/10.46298/dmtcs.3554.

Marie Albenque;Jean-Francois Marckert, 2008, Some families of increasing planar maps, Electronic Journal of Probability, 13, none, 10.1214/ejp.v13-563, https://doi.org/10.1214/ejp.v13-563.

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