Electronic Journal of Probability

Triangulating stable laminations

Igor Kortchemski and Cyril Marzouk

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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

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

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

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Zentralblatt MATH identifier

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

noncrossing trees simply generated trees geodesic laminations

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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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