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The natural paramterization or length for the Schramm-Loewner evolution (SLE{\kappa}) is the candidate for the scaling limit of the length of discrete curves for \kappa < 8.
G. Lawler and S. Sheffield (2011). A natural parametrization for the Scheramm-Loewner evolution. Annals of Probab. 39
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S. Smirnov (2001). Critical percolation in the plane: Conformal invariance, Cardy’s formula, scaling limits. C. R. Acad. Sci. Paris Ser. I Math. 333
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G. Lawler. O. Schramm, and W. Werner (2004). Conformal invariance of planar loop-erased random walks and uniform spanning trees, Annals of Probab. 32
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G. Lawler (2005). Conformally Invariant Processes in the Plane
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S. Rohde and O. Schramm (2005). Basic properties of SLE, Annals of Math. 161
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O. Schramm and S. Sheffield (2005). Harmonic explorer and its convergence to SLE(4), Annals of Probab. 33
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V. Beffara (2008). The dimension of SLE curves, Annals of Probab. 36
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J. Lind (2008). Hölder regularity of the SLE trace, Trans. Amer. Math. Soc. 360 , 7
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G. Lawler, Continuity of radial and two-sided radial SLE, preprint
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S. Lalley, G. Lawler, H. Narayanan (2009). Geometric interpretation of half-plane capacity, Electron. Comm. Probab 14
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G. Lawler (2009). Schramm-Loewner evolution, in statistical mechanics
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S. Smirnov (2009). Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model, Ann of Math. 172
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F. Johansson Viklund and G. Lawler (2011). Optimal Holder exponent for the SLE path, Duke Math. J. 159
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G. Lawler and B. Werness. Multi-point Green’s function for SLE and an estimate of Beffara, to appear in Annals of Probab
Cited in the paper.
G. Lawler and W. Zhou, SLE curves and natural parametrization, to appear in Annals of Probab
Cited in the paper.