Journal of Applied Probability

Pruned discrete random samples

Rudolf Grübel and Paweł Hitczenko

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Abstract

Let Xi,i ∈ ℕ, be independent and identically distributed random variables with values in ℕ0. We transform (`prune') the sequence {X1,...,Xn},n∈ ℕ, of discrete random samples into a sequence {0,1,2,...,Yn}, n∈ ℕ, of contiguous random sets by replacing Xn+1 with Yn +1 if Xn+1 >Yn. We consider the asymptotic behaviour of Yn as n→∞. Applications include path growth in digital search trees and the number of tables in Pitman's Chinese restaurant process if the latter is conditioned on its limit value.

Article information

Source
J. Appl. Probab. Volume 50, Number 2 (2013), 542-556.

Dates
First available in Project Euclid: 19 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1371648960

Digital Object Identifier
doi:10.1239/jap/1371648960

Mathematical Reviews number (MathSciNet)
MR3102499

Zentralblatt MATH identifier
1270.60016

Subjects
Primary: 60C05: Combinatorial probability
Secondary: 60F99: None of the above, but in this section 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Chinese restaurant process digital search trees geometric distribution maxima tail behaviour

Citation

Grübel, Rudolf; Hitczenko, Paweł. Pruned discrete random samples. J. Appl. Probab. 50 (2013), no. 2, 542--556. doi:10.1239/jap/1371648960. https://projecteuclid.org/euclid.jap/1371648960


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