A family of random trees with random edge lengths

A family of random trees with random edge lengths

Report Number
526
Authors
David Aldous and Jim Pitman
Citation
Random Structures and Algorithms Vol 15, 176-195 (1999)
Abstract

We introduce a family of probability distributions on the space of trees with I labeled vertices and possibly extra unlabeled vertices of degree 3, whose edges have positive real lengths. Formulas for distributions of quantities such as degree sequence, shape, and total length are derived. An interpretation is given in terms of sampling from the inhomogeneous continuum random tree of Aldous and Pitman (1998). Key words and phrases: continuum tree, enumeration, random tree, spanning tree, weighted tree, Cayley's multinomial expansion.

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