Addendum to "The Minimal Spanning Tree in a Complete Graph and a Functional Limit Theorem for Trees in a Random Graph"

In the article “The minimal spanning tree in a complete graph and a functional limit theorem for trees in a random graph” by Janson [6] it is shown that the minimal weight Wn of a spanning tree in a complete graph Kn with independent, uniformly distributed random weights on the edges has an asymptotic normal distribution. The same holds with exponentially distributed weights with mean 1. The mean converges, as shown in the classical paper by A. Frieze [3], to ζ(3), and the asymptotic variance is σ2/n for a positive constant σ2; more precisely, see [6, Theorem 1], n ( Wn − ζ(3) ) d −→ N(0, σ) as n→∞. The constant σ2 was given in [6] by the complicated expression