Pruned discrete random samples

Rudolf Grübel & Pawel Hitczenko
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...
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