# The CRT is the scaling limit of random dissections

Abstract : 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.
Type de document :
Article dans une revue
Random Structures and Algorithms, Wiley, 2014, pp.Online first
Domaine :

https://hal.archives-ouvertes.fr/hal-00823219
Contributeur : Bénédicte Haas <>
Soumis le : jeudi 16 mai 2013 - 13:04:34
Dernière modification le : vendredi 4 janvier 2019 - 17:32:33

### Identifiants

• HAL Id : hal-00823219, version 1
• ARXIV : 1305.3534

### Citation

Nicolas Curien, Bénédicte Haas, Igor Kortchemski. The CRT is the scaling limit of random dissections. Random Structures and Algorithms, Wiley, 2014, pp.Online first. 〈hal-00823219〉

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