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.
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Article dans une revue
Random Structures and Algorithms, Wiley, 2014, pp.Online first
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https://hal.archives-ouvertes.fr/hal-00823219
Contributeur : Bénédicte Haas <>
Soumis le : jeudi 16 mai 2013 - 13:04:34
Dernière modification le : jeudi 27 avril 2017 - 09:45:48

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

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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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