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The CRT is the scaling limit of random dissections

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Date
2015
Link to item file
https://arxiv.org/abs/1305.3534v2
Dewey
Probabilités et mathématiques appliquées
Sujet
Brownian Continuum Random Tree; Gromov–Hausdorff topology; Random dissections; Galton–Watson trees; scaling limits
Journal issue
Random Structures & Algorithms
Volume
47
Number
2
Publication date
2015
Article pages
304-327
Publisher
J. Wiley
DOI
http://dx.doi.org/10.1002/rsa.20554
URI
https://basepub.dauphine.fr/handle/123456789/11289
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Curien, Nicolas
Haas, Bénédicte
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Kortchemski, Igor
Type
Article accepté pour publication ou publié
Abstract (EN)
We study the graph structure of large random dissections of polygons sampled according to Boltzmann weights, which encompasses the case of uniform dissections or uniform $p$-angulations. As their number of vertices $n$ goes to infinity, we show that these random graphs, rescaled by $n^{-1/2}$, converge in the Gromov--Hausdorff sense towards a multiple of Aldous' Brownian tree when the weights decrease sufficiently fast. The scaling constant depends on the Boltzmann weights in a rather amusing and intriguing way, and is computed by making use of a Markov chain which compares the length of geodesics in dissections with the length of geodesics in their dual trees.

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