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
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.
Ann. Appl. Probab., Volume 18, Number 1 (2008), 288-333.
First available in Project Euclid: 9 January 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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