From trees to seeds: on the inference of the seed from large trees in   the uniform attachment model
  We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total variation point of view. To do this, we construct statistics that measure, in a certain well-defined sense, global "balancedness" properties of such trees. Our paper follows recent results on the same question for the preferential attachment model. 
S\'ebastien Bubeck, Ronen Eldan, Elchanan Mossel, Mikl\'os Z. R\'acz
math.PR cs.DM cs.SI math.ST stat.TH