Journal of Applied Probability

On tail bounds for random recursive trees

Götz Olaf Munsonius

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Abstract

We consider a multivariate distributional recursion of sum type, as arises in the probabilistic analysis of algorithms and random trees. We prove an upper tail bound for the solution using Chernoff's bounding technique by estimating the Laplace transform. The problem is traced back to the corresponding problem for binary search trees by stochastic domination. The result obtained is applied to the internal path length and Wiener index of random b-ary recursive trees with weighted edges and random linear recursive trees. Finally, lower tail bounds for the Wiener index of these trees are given.

Article information

Source
J. Appl. Probab., Volume 49, Number 2 (2012), 566-581.

Dates
First available in Project Euclid: 16 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1339878805

Digital Object Identifier
doi:10.1239/jap/1339878805

Mathematical Reviews number (MathSciNet)
MR2977814

Zentralblatt MATH identifier
1251.60009

Subjects
Primary: 60C05: Combinatorial probability 05C05: Trees 05C80: Random graphs [See also 60B20] 60E15: Inequalities; stochastic orderings

Keywords
Random tree probabilistic analysis of algorithms tail bound path length Wiener index

Citation

Munsonius, Götz Olaf. On tail bounds for random recursive trees. J. Appl. Probab. 49 (2012), no. 2, 566--581. doi:10.1239/jap/1339878805. https://projecteuclid.org/euclid.jap/1339878805


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