On Robson's convergence and boundedness conjectures concerning the height of binary search trees

On Robson's Convergence and Boundedness Conjecture Concering the Height of Binary Search Trees

Profile and Height of Random Binary Search Trees

The purpose of this article is to survey recent results on distributional properties of random binary search trees. In particular we consider the profile and the height.

Probabilistic analysis of the asymmetric digital search trees

In this paper, by applying three functional operators the previous results on the (Poisson) variance of the external profile in digital search trees will be improved. We study the profile built over $n$ binary strings generated by a memoryless source with unequal probabilities of symbols and use a combinatorial approach for studying the Poissonized variance, since the probability distribution o...

Width and Mode of the Profile for Some Random Trees of Logarithmic Height by Luc Devroye

We propose a new, direct, correlation-free approach based on central moments of profiles to the asymptotics of width (size of the most abundant level) in some random trees of logarithmic height. The approach is simple but gives precise estimates for expected width, central moments of the width, and almost sure convergence. It is widely applicable to random trees of logarithmic height, including...

P´olya Urn Models and Connections to Random Trees: A Review

This paper reviews P´olya urn models and their connection to random trees. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology: • P´olya-Eggenberger’s urn • Bernard Friedman’s urn • Generalized P´olya urns • Extended urn schemes • Invertible urn schemes ...