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We prove Russo-Seymour-Welsh-type uniform bounds on crossing probabilities for the FK Ising model at criticality, independent of the boundary conditions.
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V. Beffara, H. Duminil-Copin, S. Smirnov, Fermionic study of the 2D Ising model, in preparation (2009)
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V. Beffara, H. Duminil-Copin, S. Smirnov, The self-dual point of the 2D random cluster model is critical above q = 4 q=4 , in preparation (2009)
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W. Werner, SLEs as boundaries of clusters of Brownian loops, C.R. Math. Acad. Sci. Paris 337
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G.F. Lawler, Conformally invariant processes in the plane, AMS (2005)
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F. Camia, C.M. Newman, Two-dimensional critical percolation: the full scaling limit, Comm. Math. Phys. 268
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B.T. Graham, G.R. Grimmett, Influence and sharp-threshold theorems for monotonic measures, Ann. Probab. 34
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G.R. Grimmett, The random-cluster model , Springer, Heidelberg (2006)
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S. Smirnov, Towards conformal invariance of 2D lattice models, Proc. ICM 2006 , vol. 2, 1421-1451 (2007)
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G.R. Grimmett, Random processes on graphs and lattices , in preparation (2009)
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A. Kemppainen, On random planar curves and their scaling limits, PhD thesis (2009)
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A. Kemppainen, S. Smirnov, Random curves, scaling limits and Loewner evolutions, in preparation (2009)
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A. Kemppainen, S. Smirnov, Conformal invariance in random cluster models. III. Full scaling limit, in preparation (2009)
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G.F. Lawler, V. Limic, Random walk: a modern introduction, in preparation (2009)
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S. Smirnov, Conformal invariance in random cluster models. II. Scaling limit of the interface, in preparation (2009)
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W. Werner, Percolation et modèle d’Ising , Cours Spécialisés de la SMF 16
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