Dependence between External Path-Length and Size in Random Tries

zbMATH Open1411.68035arXiv1604.08658MaRDI QIDQ4632480

Michael Fuchs, Hsien-Kuei Hwang

Publication date: 29 April 2019

Abstract: We study the size and the external path length of random tries and show that they are asymptotically independent in the asymmetric case but strongly dependent with small periodic fluctuations in the symmetric case. Such an unexpected behavior is in sharp contrast to the previously known results that the internal path length is totally positively correlated to the size and that both tend to the same normal limit law. These two examples provide concrete instances of bivariate normal distributions (as limit laws) whose correlation is $0$, $1$ and periodically oscillating.

Full work available at URL: https://arxiv.org/abs/1604.08658

zbMATH Keywords

Mellin transformasymptotic normalitycontraction methodPearson's correlation coefficientrandom triesPoissonization/de-Poissonization

Mathematics Subject Classification ID

Analysis of algorithms (68W40) Combinatorial probability (60C05) Data structures (68P05)

Related Items (1)

Concentration of Size and Path Length of Tries

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