Convergence of uniform noncrossing partitions toward the Brownian triangulation

par Jérémie Bettinelli

jeudi 17 janv. 2019, 14:30 → 15:30 Europe/Paris

435 (ENS Lyon)

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.