## Brazilian Journal of Probability and Statistics

- Braz. J. Probab. Stat.
- Volume 31, Number 2 (2017), 215-228.

### On the critical probability of percolation on random causal triangulations

José Cerda-Hernández, Anatoly Yambartsev, and Stefan Zohren

#### Abstract

In this work, we study bond percolation on random causal triangulations. While in the sub-critical regime there is no phase transition, we show that for percolation on critical random causal triangulations there exists a non-trivial phase transition and we compute an upper bound for the critical probability. Furthermore, the critical value is shown to be almost surely constant.

#### Article information

**Source**

Braz. J. Probab. Stat., Volume 31, Number 2 (2017), 215-228.

**Dates**

Received: December 2015

Accepted: February 2016

First available in Project Euclid: 14 April 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1492156960

**Digital Object Identifier**

doi:10.1214/16-BJPS310

**Mathematical Reviews number (MathSciNet)**

MR3635903

**Zentralblatt MATH identifier**

1372.82022

**Keywords**

Percolation causal triangulations phase transition

#### Citation

Cerda-Hernández, José; Yambartsev, Anatoly; Zohren, Stefan. On the critical probability of percolation on random causal triangulations. Braz. J. Probab. Stat. 31 (2017), no. 2, 215--228. doi:10.1214/16-BJPS310. https://projecteuclid.org/euclid.bjps/1492156960