Asymptotic distribution of two-protected nodes in random binary search trees
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TLDR
The exact moments of the number of 2-protected nodes in binary search trees grown from random permutations are derived using a properly normalized version of this tree parameter.About:
This article is published in Applied Mathematics Letters.The article was published on 2012-12-01 and is currently open access. It has received 34 citations till now. The article focuses on the topics: Random binary tree & Ternary search tree.read more
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Limit laws for functions of fringe trees for binary search trees and random recursive trees
Cecilia Holmgren,Svante Janson +1 more
TL;DR: The general limit theorems for sums of functions of subtrees of (random) binary search trees and random recursive trees are proved.
Journal ArticleDOI
Protected nodes and fringe subtrees in some random trees
Luc Devroye,Svante Janson +1 more
TL;DR: Protected nodes in various classes of random rooted trees are studied by putting them in the general context of fringe subtrees introduced by Aldous (1991) to give unified and simple proofs of several earlier results, as well as new results.
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Fringe trees, Crump–Mode–Jagers branching processes and $m$-ary search trees
Cecilia Holmgren,Svante Janson +1 more
TL;DR: In this article, asymptotics of random fringe trees and extended fringe trees in random trees that can be constructed as family trees of a Crump-Mode-Jagers branching process, stopped at a suita.
Posted Content
Limit Laws for Functions of Fringe trees for Binary Search Trees and Recursive Trees
Cecilia Holmgren,Svante Janson +1 more
TL;DR: In this article, it was shown that the random recursive tree asymptotically converges to a Poisson distribution if and only if the number of copies of a fixed subtree is a constant.
Journal ArticleDOI
Asymptotic properties of protected nodes in random recursive trees
TL;DR: It follows that the number of protected nodes in a random recursive tree, upon proper scaling, converges in probability to a constant.
References
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The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
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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
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The Central Limit Theorem for Dependent Random Variables
TL;DR: The central limit theorem has been extended to the case of dependent random variables by several authors (Bruns, Markoff, S. Bernstein, P. Levy, and Loeve) as mentioned in this paper.
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Polya Urn Models
TL;DR: In this paper, a collection of modern and evolving urn theory and its numerous applications are discussed, including exchangeability, stochastic processes via urns, and functional equations for moment generating functions can be obtained and solved.
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Sorting: A Distribution Theory
TL;DR: Sorting and associated concepts insertion sort shellsort bubble sort bubble sort selection sort sorting by counting quick sort sample sort heap sort merge sort bucket sorts sorting non-random data epilogue answers to exercises a notation and standard results from probability theory.