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- Title
Random non-crossing plane configurations: A conditioned Galton-Watson tree approach.
- Authors
Curien, Nicolas; Kortchemski, Igor
- Abstract
ABSTRACT We study various models of random non-crossing configurations consisting of diagonals of convex polygons, and focus in particular on uniform dissections and non-crossing trees. For both these models, we prove convergence in distribution towards Aldous' Brownian triangulation of the disk. In the case of dissections, we also refine the study of the maximal vertex degree and validate a conjecture of Bernasconi, Panagiotou and Steger. Our main tool is the use of an underlying Galton-Watson tree structure. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 236-260, 2014
- Subjects
TREE graphs; RANDOM variables; CONVEX functions; POLYGONS; TRIANGULATION; BOHMIAN mechanics
- Publication
Random Structures & Algorithms, 2014, Vol 45, Issue 2, p236
- ISSN
1042-9832
- Publication type
Article
- DOI
10.1002/rsa.20481