The Wiener Index of Random Trees

The Wiener index is analysed for random recursive trees and random binary search trees in uniform probabilistic models. We obtain expectations, asymptotics for the variances, and limit laws for this parameter. The limit distributions are characterized as the projections of bivariate measures that satisfy certain fixed point equations. Covariances, asymptotic correlations, and bivariate limit laws for the Wiener index and the internal path length are given.

Relationships among Spearman's Rho, Kendall's Tau, and the Matching Problem

Under an hypothesis of independence it is shown that a measure of agreement for ranked data based on the matching paradigm has asymptotic correlations of zero with Spearman's rho and Kendall's tau. However, for all values of n, the Pearson correlations between each pair of indices are simply related.