@article{EJP3238,
author = {Gourab Ray},
title = {Geometry and percolation on half planar triangulations},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {half planar maps, volume growth, anchored expansion, percolation},
abstract = {We analyze the geometry of domain Markov half planar triangu-lations. In [5] 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.
},
pages = {no. 47, 1-28},
issn = {1083-6489},
doi = {10.1214/EJP.v19-3238},
url = {http://ejp.ejpecp.org/article/view/3238}}