Asymptotics of heights in Rrandom trees constructed by aggregation
Haas, Bénédicte (2017), Asymptotics of heights in Rrandom trees constructed by aggregation, Electronic Journal of Probability, 22, p. n°21. 10.1214/17-EJP31
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1606.06536v1
Journal nameElectronic Journal of Probability
Institute of Mathematical Statistics
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Abstract (EN)To each sequence (an) of positive real numbers we associate a growing sequence (Tn) of continuous trees built recursively by gluing at step n a segment of length an on a uniform point of the pre–existing tree, starting from a segment T1 of length a1. Previous works [5, 10] on that model focus on the influence of (an) on the compactness and Hausdorff dimension of the limiting tree. Here we consider the cases where the sequence (an) is regularly varying with a non–negative index, so that the sequence (Tn) explodes. We determine the asymptotics of the height of Tn and of the subtrees of Tn spanned by the root and ℓ points picked uniformly at random and independently in Tn, for all ℓ∈N.
Subjects / KeywordsRandom trees; aggregation
Showing items related by title and author.
Winkel, Matthias; Pitman, Jim; Miermont, Grégory; Haas, Bénédicte (2008-09) Article accepté pour publication ou publié