Year: 2016
Type: article
Abstract: We study the asymptotic behaviour of random simply generated noncrossing planar trees in the space of compact subsets of the unit disk, equipped with the Hausdorff distance. Their distributional limits are obtained by triangulating at random the faces of stable laminations, which are random compact subsets of the unit disk made of non-intersecting chords and which are coded by stable Lévy processes. We also study other ways to “fill-in” the faces of stable laminations, which leads us to introduce the iteration of laminations and of trees.
DOI: 10.1214/16-ejp4559
Authors: Igor Kortchemski, Cyril Marzouk
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $675
OpenAlex ID: W2222733583