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June 2014 Search trees: Metric aspects and strong limit theorems
Rudolf Grübel
Ann. Appl. Probab. 24(3): 1269-1297 (June 2014). DOI: 10.1214/13-AAP948

Abstract

We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces converge with probability 1. This is then used to obtain almost sure convergence for various tree functionals, together with representations of the respective limit random variables as functions of the limit tree.

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Rudolf Grübel. "Search trees: Metric aspects and strong limit theorems." Ann. Appl. Probab. 24 (3) 1269 - 1297, June 2014. https://doi.org/10.1214/13-AAP948

Information

Published: June 2014
First available in Project Euclid: 23 April 2014

zbMATH: 1294.60009
MathSciNet: MR3199986
Digital Object Identifier: 10.1214/13-AAP948

Subjects:
Primary: 60B99
Secondary: 05C05, 60J10, 68Q25

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.24 • No. 3 • June 2014
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