University thesis:
Freiburg (Breisgau), Univ., Diss., 2010
Footnote:
Description:
The first part is devoted to the analysis of random b-ary recursive trees with weighted edges. We investigate functionals related to distances with regard to limit theorems. We show central limit theorems for the depth of a random node and distances between two random nodes. Further, we prove limit theorems for the internal path length, the Wiener index and its generalisation -- the total Steiner k-distance -- with the aid of the contraction method using recursion formulae. To do this, the asymptotic expansion of the expectation of the considered functionals has to be determined. Moreover, an upper tail bound for the distribution of the total Steiner k-distance is proved by considering the Laplace transform. A lower tail bound is shown for the Wiener index ...