Conditioned multi-type Galton−Watson trees
نویسندگان
چکیده
منابع مشابه
Noncrossing trees are almost conditioned Galton-Watson trees
A non-crossing tree (NC-tree) is a tree drawn on the plane having as vertices a set of points on the boundary of a circle, and whose edges are straight line segments that do not cross. In this paper, we show that NC-trees with size n are conditioned Galton–Watson trees. As corollaries, we give the limit law of depth-first traversal processes and the limit profile of NC-trees.
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The trees that we consider are rooted and ordered (= plane); thus each node v has a number of children, ordered in a sequence v1, . . . , vd, where d = d(v) ≥ 0 is the outdegree of v. (See [1] for more information on these and other types of trees; the trees we consider are there called planted plane trees.) We let Tn denote the set of all ordered rooted trees with n nodes (including the root) ...
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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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ژورنال
عنوان ژورنال: ESAIM: Probability and Statistics
سال: 2016
ISSN: 1292-8100,1262-3318
DOI: 10.1051/ps/2016019