Electronic Journal of Probability

Triangulating stable laminations

Igor Kortchemski and Cyril Marzouk

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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.

Article information

Source
Electron. J. Probab., Volume 21 (2016), paper no. 11, 31 pp.

Dates
Received: 16 September 2015
Accepted: 26 January 2016
First available in Project Euclid: 15 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1455559938

Digital Object Identifier
doi:10.1214/16-EJP4559

Mathematical Reviews number (MathSciNet)
MR3485353

Zentralblatt MATH identifier
1338.05249

Subjects
Primary: 05C80: Random graphs [See also 60B20] 60C05: Combinatorial probability
Secondary: 05C05: Trees 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
noncrossing trees simply generated trees geodesic laminations

Rights
Creative Commons Attribution 4.0 International License.

Citation

Kortchemski, Igor; Marzouk, Cyril. Triangulating stable laminations. Electron. J. Probab. 21 (2016), paper no. 11, 31 pp. doi:10.1214/16-EJP4559. https://projecteuclid.org/euclid.ejp/1455559938


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