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Article Dans Une Revue Seminaire Lotharingien de Combinatoire Année : 2018

Convergence of uniform noncrossing partitions toward the Brownian triangulation

Résumé

We give a short proof that a uniform noncrossing partition of the regular n-gon weakly converges toward Aldous's Brownian triangulation of the disk, in the sense of the Hausdorff topology. This result was first obtained by Curien & Kortchemski, using a more complicated encoding. Thanks to a result of Marchal on strong convergence of Dyck paths toward the Brownian excursion, we furthermore give an algorithm that allows to recursively construct a sequence of uniform noncrossing partitions for which the previous convergence holds almost surely. In addition, we also treat the case of uniform noncrossing pair partitions of even-sided polygons.
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hal-02347506 , version 1 (05-11-2019)

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  • HAL Id : hal-02347506 , version 1

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Jérémie Bettinelli. Convergence of uniform noncrossing partitions toward the Brownian triangulation. Seminaire Lotharingien de Combinatoire, 2018. ⟨hal-02347506⟩
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