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Random records and cuttings in binary search trees. (English) Zbl 1215.05162
Summary: We study the number of random records in a binary search tree with \(n\) vertices (or equivalently, the number of cuttings required to eliminate the tree). We show that a classical limit theorem for convergence of sums of triangular arrays to infinitely divisible distributions can be used to determine the distribution of this number. The asymptotic distribution of the (normalized) number of records or cuts is found to be weakly 1-stable.

05C80 Random graphs (graph-theoretic aspects)
05C05 Trees
60F99 Limit theorems in probability theory
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