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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, 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 hyperscaling ideas developed by Kesten.
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Contributor : Pierre Nolin <>
Submitted on : Friday, December 22, 2006 - 3:20:38 PM
Last modification on : Friday, July 2, 2021 - 3:46:34 AM
Long-term archiving on: : Monday, September 20, 2010 - 5:51:15 PM


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Pierre Nolin. Critical Exponents of Planar Gradient Percolation. 2006. ⟨hal-00109036v2⟩



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