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For random collections of self-avoiding loops in two-dimensional domains, we define a simple and natural conformal restriction property that is conjecturally satisfied by the scaling limits of interfaces in models from statistical physics.
The fractal geometry of nature
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G.F. Lawler, O. Schramm, W. Werner (2003), Conformal invariance of planar loop-erased random walks and uniform spanning trees, Ann. Probab. 92
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G.F. Lawler, O. Schramm, W. Werner (2003), Conformal restriction properties. The chordal case, J. Amer. Math. Soc. 16
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B. Doyon (2009), Conformal loop ensembles and the stress-energy tensor. I. Fundamental notions of CLE, preprint
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B. Doyon (2009), Conformal loop ensembles and the stress-energy tensor. II. Construction of the stress-energy tensor, preprint
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J. Dubédat (2009), SLE and the Free Field: Partition functions and couplings, J. Amer. Math. Soc. 22
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Geometric Interpretation of Half-Plane Capacity
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O. Schramm, S. Sheffield (2005), Harmonic explorer and its convergence to SLE4, Ann. Probab. 33
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O. Schramm, D.B. Wilson (2005), SLE coordinate changes, New York J. Math. 11
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W. Werner (2005), Conformal restriction and related questions, Probability Surveys 2
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F. Camia, C. Newman (2006), Two-dimensional critical percolation: The full scaling limit, Comm. Math. Phys. 268
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S. Smirnov (2007), Towards conformal invariance of 2D lattice models, Proc. ICM 2006, vol. 2, 1421-1451
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W. Werner (2006), Some recent aspects of random conformally invariant systems, in Les Houches Summer School, Session LXXXIII, Mathematical statistical mechanics, 57-99, Elsevier
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2009
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J.-F. Le Gall, G. Miermont (2009), Scaling limits of random planar maps with large faces. Ann. Probab., to appear
2009
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O. Schramm, S. Sheffield (2009), Contour lines of the two-dimensional discrete Gaussian Free Field, Acta Math. 202
2009
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O. Schramm, S. Sheffield, D.B. Wilson (2009), Conformal radii in conformal loop ensembles, Comm. Math. Phys. 288
2009
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S. Sheffield (2009), Exploration trees and conformal loop ensembles, Duke Math. J. 147
2009
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D. Chelkak, S. Smirnov (2010), Conformal invariance of the Ising model at criticality, preprint
2010
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J. Miller (2010), Fluctuations for the Ginzburg-Landau ∇ ϕ \nabla\phi Interface Model on a Bounded Domain, preprint
2010
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J. Miller (2010), Universality for SLE(4), preprint
2010
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O. Schramm, S. Sheffield, A contour line of the continuum Gaussian Free Field, preprint, 2010
2010
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O. Schramm, S. Smirnov (2010), On the scaling limits of planar percolation, preprint
2010
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S. Sheffield and N. Sun (2010), Strong path convergence from Loewner driving convergence, preprint
2010
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S. Smirnov (2010), Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model, Ann. Math. 172
2010
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N. Sun (2010), Conformally invariant scaling limits in planar critical percolation, preprint
2010
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