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1 results

  • Pruned Discrete Random Samples

  • Part of
  • Rudolf Grübel, Paweł Hitczenko
  • Journal:
    Journal of Applied Probability / Volume 50 / Issue 2 / June 2013
    Published online by Cambridge University Press:
    30 January 2018, pp. 542-556
    Print publication:
    June 2013
    • Article
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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.