Uniform attachment with freezing

Abstract

In the classical model of random recursive trees, trees are recursively built by attaching new vertices to old ones. What happens if vertices are allowed to freeze, in the sense that new vertices cannot be attached to already frozen ones? We are interested in the impact of freezing on the height of such trees.

42 pages, 10 figures, 2 animations, part one of a two-paper series, revised final version to appear in Ann. Appl. Probab