Electronic Journal of Probability
- Electron. J. Probab.
- Volume 19 (2014), paper no. 47, 28 pp.
Geometry and percolation on half planar triangulations
We analyze the geometry of domain Markov half planar triangulations. In  it is shown thatthere exists a one-parameter family ofmeasures supported on half planar triangulations satisfying translation invariance and domain Markov property. We study the geometry of these maps and show that they exhibit a sharp phase-transition inview of their geometry atα = 2/3. For α < 2/3, the maps form atree-like stricture with infinitely many small cut-sets.For α > 2/3,we obtain maps of hyperbolic nature with exponential growth andanchoredexpansion. Some results about the geometry of percolation clusters on such maps and random walk on them are also obtained.
Electron. J. Probab., Volume 19 (2014), paper no. 47, 28 pp.
Accepted: 31 May 2014
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60B05: Probability measures on topological spaces
This work is licensed under a Creative Commons Attribution 3.0 License.
Ray, Gourab. Geometry and percolation on half planar triangulations. Electron. J. Probab. 19 (2014), paper no. 47, 28 pp. doi:10.1214/EJP.v19-3238. https://projecteuclid.org/euclid.ejp/1465065689