From trees to seeds: On the inference of the seed from large trees in the uniform attachment model

Sébastien Bubeck, Ronen Eldan, Elchanan Mossel, Miklós Z. Rácz
2017 Bernoulli  
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. 1 2 x∈X |µ
more » ... model. 1 2 x∈X |µ (x) − ν (x)|. Our main result shows that each seed leads to a unique limiting distribution of the uniform attachment tree.
doi:10.3150/16-bej831 fatcat:pz5woejusrd6ngzchur4zem2me