Dependence between path-length and size in random digital trees. (30th November 2017)

• Record Type: Journal Article
• Authors: Fuchs, Michael; Hwang, Hsien-Kuei
• Is Part Of: Journal of applied probability. Volume 54:Number 4(2017)
• Page Start: 1125
• Page End: 1143
• Publication Date: 2017-11-30
• Subjects: Random tries, -- covariance, -- total path length, -- Pearson's correlation coefficient, -- asymptotic normality, -- Poissonization, -- de-Poissonization, -- integral transform, -- contraction method; Primary 05A16, -- 60F05, -- 68W40, -- Secondary 60C05, -- 68P05; 519.2
• DOI: 10.1017/jpr.2017.56
• Languages: English
• ISSNs: 0021-9002

Abstract

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 on random tries, that the size is totally positively correlated to the internal path length and that both tend to the same normal limit law. These two dependence examples provide concrete instances of bivariate normal distributions (as limit laws) whose components have correlation either zero or one or periodically oscillating. Moreover, the same type of behavior is also clarified for other classes of digital trees such as bucket digital trees and Patricia tries.