We characterize the limiting behavior of the number of nodes in level k of binary search trees Tₙ in the central region 1.2 log n ≤ 2.8 log n. Especially we show that the width V̄ₙ (the maximal number of internal nodes at the same level) satisfies V̄ₙ ~ (n/√4πlog n) as n → ∞ a.s.
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Chauvin et al. (2001) studied this question.
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