Journal of Applied Probability

Pruned discrete random samples

Rudolf Grübel and Paweł Hitczenko

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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

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

First available in Project Euclid: 19 June 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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)

Chinese restaurant process digital search trees geometric distribution maxima tail behaviour


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

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