English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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, inthe sense of the Hausdorff topology. This result was first obtained by Curien &Kortchemski, using a more complicated encoding. Thanks to a result of Marchalon strong convergence of Dyck paths toward the Brownian excursion, wefurthermore give an algorithm that allows to recursively construct a sequenceof uniform noncrossing partitions for which the previous convergence holdsalmost surely.  In addition, we also treat the case of uniform noncrossing pair partitions ofeven-sided polygons.

Convergence of uniform noncrossing partitions toward the Brownian triangulation