## Bernoulli

- Bernoulli
- 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

Sébastien Bubeck, Ronen Eldan, Elchanan Mossel, and Miklós Z. Rácz

#### 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.

#### Article information

**Source**

Bernoulli, Volume 23, Number 4A (2017), 2887-2916.

**Dates**

Received: July 2015

First available in Project Euclid: 9 May 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.bj/1494316836

**Digital Object Identifier**

doi:10.3150/16-BEJ831

**Mathematical Reviews number (MathSciNet)**

MR3648049

**Zentralblatt MATH identifier**

1381.60026

**Keywords**

random trees seed tree statistical inference uniform attachment

#### Citation

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