Critical exponents of planar gradient percolation

Details Critical exponents of planar gradient percolation Critical exponents of planar gradient percolation

2006-10-23

arxiv.org/abs/math/0610682v3

Annals of Probability 2008, Vol. 36, No. 5, 1748-1776

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AOP375 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/07-AOP375

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.

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