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From trees to seeds: on the inference of the seed from large trees in the uniform attachment model
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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.
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Subcritical percolation and network archaeology on random recursive tree substrate networks
For random recursive trees with independent Erdős–Rényi shortcut edges, subcritical bond percolation exposes a decorated tree structure on which Jordan centrality recovers the root within a deterministic-size confidence set.
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