Critical exponents of planar gradient percolation
Abstract
We study gradient percolation for site percolation on the triangular lattice. This is a percolation model where the percolation probability depends linearly on the location of the site. We prove the results predicted by physicists for this model. More precisely, we describe the fluctuations of the interfaces around their (straight) scaling limits, and the expected and typical lengths of these interfaces. These results build on the recent results for critical percolation on this lattice by Smirnov, Lawler, Schramm and Werner, and on the scaling ideas developed by Kesten.
Keywords
Cite
@article{arxiv.math/0610682,
title = {Critical exponents of planar gradient percolation},
author = {Pierre Nolin},
journal= {arXiv preprint arXiv:math/0610682},
year = {2008}
}
Comments
Published in at http://dx.doi.org/10.1214/07-AOP375 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)