Random non-crossing plane configurations: A conditioned Galton-Watson tree approach
نویسندگان
چکیده
منابع مشابه
Random non-crossing plane configurations: A conditioned Galton-Watson tree approach
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 ...
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We give a necessary and sufficient condition for the convergence in distribution of a conditioned Galton-Watson tree to Kesten’s tree. This yields elementary proofs of Kesten’s result as well as other known results on local limit of conditioned Galton-Watson trees. We then apply this condition to get new results, in the critical and sub-critical cases, on the limit in distribution of a Galton-W...
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A conditioned Galton–Watson tree is a random rooted tree that is (or has the same distribution as) the family tree of a Galton–Watson process with some given offspring distribution, conditioned on the total number of vertices. We let ξ be a random variable with the given offspring distribution; i.e., the number of offspring of each individual in the Galton–Watson process is a copy of ξ. We let ...
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We revisit several maximization problems for geometric networks design under the non-crossing constraint, first studied by Alon, Rajagopalan and Suri (ACM Symposium on Computational Geometry, 1993). Given a set of n points in the plane in general position (no three points collinear), compute a longest non-crossing configuration composed of straight line segments that is: (a) a matching (b) a Ha...
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We consider random walks with a bias toward the root on the family tree T of a supercritical Galton-Watson branching process and show that the speed is positive whenever the walk is transient. The corresponding harmonic measures are carried by subsets of the boundary of dimension smaller than that of the whole boundary. When the bias is directed away from the root and the extinction probability...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2012
ISSN: 1042-9832
DOI: 10.1002/rsa.20481