## Journal of Applied Probability

- J. Appl. Probab.
- Volume 50, Number 3 (2013), 603-611.

### Almost giant clusters for percolation on large trees with logarithmic heights

#### Abstract

This paper is based on works presented at the 2012 Applied Probability Trust Lecture in Sheffield; its main purpose is to survey the recent asymptotic results of Bertoin (2012a) and Bertoin and Uribe Bravo (2012b) about Bernoulli bond percolation on certain large random trees with logarithmic height. We also provide a general criterion for the existence of giant percolation clusters in large trees, which answers a question raised by David Croydon.

#### Article information

**Source**

J. Appl. Probab. Volume 50, Number 3 (2013), 603-611.

**Dates**

First available in Project Euclid: 5 September 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1378401225

**Digital Object Identifier**

doi:10.1239/jap/1378401225

**Mathematical Reviews number (MathSciNet)**

MR3102504

**Zentralblatt MATH identifier**

1283.60119

**Subjects**

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 05C05: Trees

**Keywords**

Random tree percolation giant component

#### Citation

Bertoin, Jean. Almost giant clusters for percolation on large trees with logarithmic heights. J. Appl. Probab. 50 (2013), no. 3, 603--611. doi:10.1239/jap/1378401225. https://projecteuclid.org/euclid.jap/1378401225