Geodesic
Convergence of Uniform Noncrossing Partitions Toward the Brownian Triangulation
Séminaire lotharingien de combinatoire, 80B (2018)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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. 

@article{SLC_2018_80B_a37,
     author = {J\'er\'emie Bettinelli},
     title = {Convergence of {Uniform} {Noncrossing} {Partitions} {Toward} the {Brownian} {Triangulation}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a37/}
}
TY  - JOUR
AU  - Jérémie Bettinelli
TI  - Convergence of Uniform Noncrossing Partitions Toward the Brownian Triangulation
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a37/
ID  - SLC_2018_80B_a37
ER  - 
%0 Journal Article
%A Jérémie Bettinelli
%T Convergence of Uniform Noncrossing Partitions Toward the Brownian Triangulation
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a37/
%F SLC_2018_80B_a37
Jérémie Bettinelli. Convergence of Uniform Noncrossing Partitions Toward the Brownian Triangulation. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a37/