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33

SIAMCOMP
2002

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Limit Laws for Sums of Functions of Subtrees of Random Binary Search Trees

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Limit Laws for Sums of Functions of Subtrees of Random Binary Search Trees

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We consider sums of functions of subtrees of a random binary search tree, and obtain general laws of large numbers and central limit theorems. These sums correspond to random recurrences of the quicksort type, Xn L = XIn +Xn-1-In +Yn, n 1, where In is uniformly distributed on {0, 1, . . . , n - 1}, Yn is a given random variable, Xk L = Xk for all k, and given In, XIn and Xn-1-In are independent. Conditions are derived such that (Xn -

Luc Devroye

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Added	23 Dec 2010
Updated	23 Dec 2010
Type	Journal
Year	2002
Where	SIAMCOMP
Authors	Luc Devroye

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