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ISSN 1088-6834(e) ISSN 0894-0347(p)

Asymmetry of near-critical percolation interfaces

Author(s): Pierre Nolin; Wendelin Werner
Journal: J. Amer. Math. Soc. 22 (2009), 797-819.
MSC (2000): Primary 60K35, 82B27, 82B43
Posted: September 16, 2008
MathSciNet review: 2505301
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Abstract | References | Similar articles | Additional information

Abstract: We study the possible scaling limits of percolation interfaces in two dimensions on the triangular lattice. When one lets the percolation parameter vary with the size of the box that one is considering, three possibilities arise in the large-scale limit. It is known that when does not converge to fast enough, then the scaling limits are degenerate, whereas if goes to zero quickly, the scaling limits are SLE(6) as when . We study some properties of the (non-void) intermediate regime where the large scale behavior is neither SLE(6) nor degenerate. We prove that in this case, the law of any scaling limit is singular with respect to that of SLE(6), even if it is still supported on the set of curves with Hausdorff dimension equal to .

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