Pruned discrete random samples

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 Pitmanʼs Chinese restaurant process if the latter is conditioned on its limit value.