Journal of Applied Probability
- J. Appl. Probab.
- Volume 49, Number 2 (2012), 566-581.
On tail bounds for random recursive trees
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.
J. Appl. Probab. Volume 49, Number 2 (2012), 566-581.
First available in Project Euclid: 16 June 2012
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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.