Triangulating stable laminations

Abstract

We study the asymptotic behavior 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 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.

34 pages, 5 figures

References in corpus (3)

• The coding of compact real trees by real valued functions
• A limit theorem for the contour process of conditioned Galton-Watson trees
• Processes iterated ad libitum

Cited by in corpus (2)

• On scaling limits of multitype Galton-Watson trees with possibly infinite variance
• Convergence of uniform noncrossing partitions toward the Brownian triangulation