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We study the size and the external path length of random tries and show thatthey are asymptotically independent in the asymmetric case but stronglydependent with small periodic fluctuations in the symmetric case. Such anunexpected behavior is in sharp contrast to the previously known results onrandom tries that the size is totally positively correlated to the internalpath length and that both tend to the same normal limit law. These twodependence examples provide concrete instances of bivariate normaldistributions (as limit laws) whose correlation is $0$, $1$ and periodicallyoscillating. Moreover, the same type of behaviors is also clarified for otherclasses of digital trees such as bucket digital trees and Patricia tries.

Dependence between Path-length and Size in Random Digital Trees