Title: Dependence between Path-length and Size in Random Digital Trees,
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 correlation is $0$, $1$ and periodically
oscillating. Moreover, the same type of behaviors is also clarified for other
classes of digital trees such as bucket digital trees and Patricia tries.