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Convergence of uniform noncrossing partitions toward the Brownian triangulation. (arXiv:1711.04872v2 [math.PR] UPDATED)
来源于:arXiv
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. 查看全文>>