Journal ArticleDOI
An analytic approach to the height of binary search trees II
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It is shown that all centralized absolute moments of the height of binary search trees of size and saturation level and of the saturation level of H<inf>n</inf>′ are bounded.Abstract:
It is shown that all centralized absolute moments EvHn − EHnvα (α ≥ 0) of the height Hn of binary search trees of size n and of the saturation level Hn′ are bounded. The methods used rely on the analysis of a retarded differential equation of the form Φ′(u) = −α−2Φ(u/α)2 with α > 1. The method can also be extended to prove the same result for the height of m-ary search trees. Finally the limiting behaviour of the distribution of the height of binary search trees is precisely determined.read more
Citations
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Minima in branching random walks
Louigi Addario-Berry,Bruce Reed +1 more
TL;DR: In this article, the authors proved exponential tail bounds for the branching random walk with bounded branching and step size under general conditions on branching random walks, and showed that the possible behavior of EM_n can be characterized to within O(1) of the minimum position of any member of the first generation.
Journal ArticleDOI
The height of a random binary search tree
TL;DR: It is shown that there exist constants α = 4.311… and β = 1.953 such that E(Hn ln n − β(i) ln n + O(1), and thatVar(H) = O(1), which indicates the height of a random binary search tree on H(n) nodes.
Journal ArticleDOI
Minima in branching random walks
Louigi Addario-Berry,Bruce Reed +1 more
TL;DR: In this paper, the authors proved exponential tail bounds for the branching random walk with bounded branching and step size under general conditions on branching random walks, where the minimum position of any member of the nth generation can be computed to within O(1) time.
Journal ArticleDOI
Tightness for a family of recursion equations
TL;DR: In this paper, the tightness of solutions for a family of recursion equations arising naturally in the study of random walks on tree-like structures was studied, including the maximal displacement of a branching random walk in one dimension and the cover time of a symmetric simple random walk on regular binary trees.
Journal ArticleDOI
Extreme Value Statistics and Traveling Fronts: Various Applications
TL;DR: In this paper, a short review of the connection between extreme value statistics and traveling fronts has been found recently in a number of diverse problems and their application in a variety of applications.
References
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An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
Journal ArticleDOI
An Introduction to Probability Theory and Its Applications.
An Introduction To Probability Theory And Its Applications
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
Book
Evolution of random search trees
TL;DR: Time Series: The Asymptotic Distribution of Auto-Correlation Coefficients On a Test of Serial Correlation for Regression Models with Lagged Dependent Variables