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

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2887-2916
Number of pages30
JournalBernoulli
Volume23
Issue number4A
DOIs
StatePublished - Nov 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Keywords

  • Random trees
  • Seed tree
  • Statistical inference
  • Uniform attachment

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