- Volume 23, Number 4A (2017), 2887-2916.
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.
Bernoulli Volume 23, Number 4A (2017), 2887-2916.
Received: July 2015
First available in Project Euclid: 9 May 2017
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Bubeck, Sébastien; Eldan, Ronen; Mossel, Elchanan; Rácz, Miklós Z. From trees to seeds: On the inference of the seed from large trees in the uniform attachment model. Bernoulli 23 (2017), no. 4A, 2887--2916. doi:10.3150/16-BEJ831. https://projecteuclid.org/euclid.bj/1494316836