The law of the iterated logarithm for the path length in random binary search trees.
Year: 2014
Type: preprint
Abstract: For a martingale $(X_n)$ converging almost surely to a random variable $X$, the sequence $(X_n - X)$ is called martingale tail sum. Recently, Neininger [Random Structures Algorithms, 46 (2015), 346-361] proved a central limit theorem for the martingale tail sum of R{e}gnier's martingale for the path length in random binary search trees. Gr{u}bel and Kabluchko [to appear in Annals of Applied Probability, (2016), arXiv 1410.0469] gave an alternative proof also conjecturing a corresponding law of the iterated logarithm. We prove the central limit theorem with convergence of higher moments and the law of the iterated logarithm for a family of trees containing binary search trees, recursive trees and plane-oriented recursive trees.
Source: arXiv (Cornell University)
Author: Henning Sulzbach
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1507842836