June 2012 On tail bounds for random recursive trees
Götz Olaf Munsonius
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J. Appl. Probab. 49(2): 566-581 (June 2012). DOI: 10.1239/jap/1339878805

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.

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Götz Olaf Munsonius. "On tail bounds for random recursive trees." J. Appl. Probab. 49 (2) 566 - 581, June 2012. https://doi.org/10.1239/jap/1339878805

Information

Published: June 2012
First available in Project Euclid: 16 June 2012

zbMATH: 1251.60009
MathSciNet: MR2977814
Digital Object Identifier: 10.1239/jap/1339878805

Subjects:
Primary: 05C05 , 05C80 , 60C05 , 60E15

Keywords: path length , Probabilistic analysis of algorithms , Random tree , tail bound , Wiener index

Rights: Copyright © 2012 Applied Probability Trust

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Vol.49 • No. 2 • June 2012
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