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Developing the theory of two-sided radial and chordal $\mathit{SLE}$, we prove that the natural parametrization on $\mathit{SLE}_{\kappa}$ curves is well defined for all $\kappa<8$.
Lawler, Gregory F.G. F. andSheffield, ScottS. (2011). A natural parametrization for the Schramm–Loewner evolution. Ann. Probab. 39 1896–1937
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Lawler, Gregory F.G. F., Schramm, OdedO. andWerner, WendelinW. (2004). Conformal invariance of planar loop-erased random walks and uniform spanning trees. Ann. Probab. 32 939–995
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Werner, WendelinW. (2004). Random planar curves and Schramm–Loewner evolutions. In Lectures on Probability Theory and Statistics. Lecture Notes in Math. 1840 107–195. Springer, Berlin
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Cardy, JohnJ. (2005). SLE for theoretical physicists. Ann. Physics 318 81–118
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Lawler, Gregory F.G. F. (2005). Conformally Invariant Processes in the Plane. Mathematical Surveys and Monographs 114. Amer. Math. Soc., Providence, RI
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Beffara, VincentV. (2008). The dimension of the SLE curves. Ann. Probab. 36 1421–1452
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Lawler, G.G. (2009). Schramm–Loewner evolution (SLE). In Statistical Mechanics (S. Sheffield and T. Spencer, eds.). IAS/Park City Mathematics Series 16 231–295. Amer. Math. Soc., Providence, RI
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Schramm, OdedO. andSheffield, ScottS. (2009). Contour lines of the two-dimensional discrete Gaussian free field. Acta Math. 202 21–137
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Schramm, OdedO. andZhou, WangW. (2010). Boundary proximity of SLE. Probab. Theory Related Fields 146 435–450
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Smirnov, StanislavS. (2010). Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model. Ann. of Math. (2) 172 1435–1467
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Cited alongside, same era.
Rohde, SteffenS. andSchramm, OdedO. (2005). Basic properties of SLE. Ann. of Math. (2) 161 883–924
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Lawler, F.F. andWerness, B.B. (2013). Multi-point Green’s functions for SLE and an estimate of Beffara. Ann. Probab. 41 1513–1555
2013
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