## Convergence of uniform noncrossing partitions toward the Brownian triangulation. (arXiv:1711.04872v2 [math.PR] UPDATED)

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 &amp; 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.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 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.