Electronic Journal of Probability
- Electron. J. Probab.
- Volume 20 (2015), paper no. 129, 45 pp.
Universal aspects of critical percolation on random half-planar maps
We study a large class of Bernoulli percolation models on random lattices of the half-plane, obtained as local limits of uniform planar triangulations or quadrangulations. We first compute the exact value of the site percolation threshold in the quadrangular case using the so-called peeling techniques. Then, we generalize a result of Angel about the scaling limit of crossing probabilities, that are a natural analogue to Cardy’s formula in (non-random) plane lattices. Our main result is that those probabilities are universal, in the sense that they do not depend on the percolation model neither on the degree of the faces of the map.
Electron. J. Probab., Volume 20 (2015), paper no. 129, 45 pp.
Received: 6 January 2015
Accepted: 7 December 2015
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 05C80: Random graphs [See also 60B20]
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K37: Processes in random environments
This work is licensed under aCreative Commons Attribution 3.0 License.
Richier, Loïc. Universal aspects of critical percolation on random half-planar maps. Electron. J. Probab. 20 (2015), paper no. 129, 45 pp. doi:10.1214/EJP.v20-4041. https://projecteuclid.org/euclid.ejp/1465067235