Brazilian Journal of Probability and Statistics

On the critical probability of percolation on random causal triangulations

José Cerda-Hernández, Anatoly Yambartsev, and Stefan Zohren

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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


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