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+X ′ n−1−In+Yn, n ≥ 1, where In is uniformly distributed on {0, 1, . . . , n− 1}, Yn is a given random variable, Xk L = X ′ k for all k, and given In, XIn and X ′ n−1−In are ind...

A recurrence is a recursive description of a function, usually of the form F : IN→ IR, or a description of such a function in terms of itself. Like all recursive structures, a recurrence consists of one or more base cases and one or more recursive cases. Each of these cases is an equation or inequality, with some function value f (n) on the left side. The base cases give explicit values for a (...