### Building uniform subtrees of a Cayley tree

Malwina Luczak
*Cambridge*
(Joint work with Peter
Winkler, Bell Labs)

We prove the existence of, and describe, a (random) process
which builds subtrees of a Cayley tree one node at a time, in such a way
that the subtree created at stage *n* is precisely a uniformly random
subtree of size *n*.