The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 18, Number 1 (2008), 288-333.
A functional limit theorem for the profile of search trees
Michael Drmota, Svante Janson, and Ralph Neininger
Abstract
We study the profile Xn,k of random search trees including binary search trees and m-ary search trees. Our main result is a functional limit theorem of the normalized profile for k=⌊αlogn⌋ in a certain range of α.
A central feature of the proof is the use of the contraction method to prove convergence in distribution of certain random analytic functions in a complex domain. This is based on a general theorem concerning the contraction method for random variables in an infinite-dimensional Hilbert space. As part of the proof, we show that the Zolotarev metric is complete for a Hilbert space.
Article information
Source
Ann. Appl. Probab., Volume 18, Number 1 (2008), 288-333.
Dates
First available in Project Euclid: 9 January 2008
Permanent link to this document
https://projecteuclid.org/euclid.aoap/1199890024
Digital Object Identifier
doi:10.1214/07-AAP457
Mathematical Reviews number (MathSciNet)
MR2380900
Zentralblatt MATH identifier
1143.68019
Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 68Q25: Analysis of algorithms and problem complexity [See also 68W40] 68P10: Searching and sorting 60C05: Combinatorial probability
Keywords
Functional limit theorem search trees profile of trees random trees analysis of algorithms
Citation
Drmota, Michael; Janson, Svante; Neininger, Ralph. A functional limit theorem for the profile of search trees. Ann. Appl. Probab. 18 (2008), no. 1, 288--333. doi:10.1214/07-AAP457. https://projecteuclid.org/euclid.aoap/1199890024