Distances and Finger Search in Random Binary Search Trees

For the random binary search tree with n nodes inserted the number of ancestors of the elements with ranks k and ℓ, 1 ≤ k < ℓ ≤ n, as well as the path distance between these elements in the tree are considered. For both quantities central limit theorems for appropriately rescaled versions are derived. For the path distance the condition ℓ − k → ∞ as n → ∞ is required. We obtain tail bounds and the order of higher moments for the path distance. The path distance measures the complexity of finger search in the tree