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September 2008 Critical exponents of planar gradient percolation
Pierre Nolin
Ann. Probab. 36(5): 1748-1776 (September 2008). DOI: 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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Pierre Nolin. "Critical exponents of planar gradient percolation." Ann. Probab. 36 (5) 1748 - 1776, September 2008.


Published: September 2008
First available in Project Euclid: 11 September 2008

zbMATH: 1187.60086
MathSciNet: MR2440922
Digital Object Identifier: 10.1214/07-AOP375

Primary: 60K35 , 82B27 , 82B43

Keywords: Critical exponents , gradient percolation , Inhomogeneous percolation , random interface

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 5 • September 2008
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