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• W3083134037 abstract "We study depth properties of a general class of random recursive trees where each node i attaches to the random node documentclass{article} usepackage{mathrsfs, amsmath, amssymb}pagestyle{empty} begin{document} begin{align*}leftlfloor iX_irightrfloorend{align*} end{document} and X0,…,Xn is a sequence of i.i.d. random variables taking values in [0,1). We call such trees scaled attachment random recursive trees (sarrt). We prove that the typical depth Dn, the maximum depth (or height) Hn and the minimum depth Mn of a sarrt are asymptotically given by Dn ∼μ-1 log n, Hn ∼ αmax log n and Mn ∼ αmin log n where μ,αmax and αmin are constants depending only on the distribution of X0 whenever X0 has a density. In particular, this gives a new elementary proof for the height of uniform random recursive trees Hn ∼ elog n that does not use branching random walks.© 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011" @default.
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• W3083134037 date "2011-12-23" @default.
• W3083134037 modified "2023-10-17" @default.
• W3083134037 title "Depth Properties of scaled attachment random recursive trees" @default.
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• W3083134037 doi "https://doi.org/10.1002/rsa.20391" @default.
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