ABSTRACT:
Give the edges of the complete graph K_n independent uniformly distributed edge weights, and let M_n be the resulting minimum spanning tree.
What can be said about the structure of M_n? A classic result of Alan Frieze is that the total weight of M_n converges to zeta(3) as n-->infinity.
We rather focus on the metric space structure of M_n, bounding its diameter and discussing its graph-theoretic distributional properties.
In particular, we will outline a proof that M_n typically has diameter of order the cube root of n; this in particular distinguishes M_n from a
uniformly random spanning tree of K_n, which has typical diameter of order the square root of n.
BIO:
Louigi Addario-Berry is an assistant professor at McGill University. Previously, he held an assistant professorship at Université de Montreal
and a Marie Curie research fellowship at the University of Oxford. http://www.math.mcgill.ca/louigi/