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In this paper, we provide a framework of estimates for describing 2D scaling limits by Schramm's SLE curves.
Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I
K. Löwner · 1923
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Conformal invariants: topics in geometric function theory
L. V. Ahlfors · 1973
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Univalent functions
P. L. Duren · 1983
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Boundary behaviour of conformal maps
C. Pommerenke · 1992
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Probability: theory and examples
R. Durrett · 1996
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Scaling limits for minimal and random spanning trees in two dimensions
M. Aizenman, A. Burchard, C. M. Newman, and D. B. Wilson · 1997
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Hölder regularity and dimension bounds for random curves
M. Aizenman and A. Burchard · 1999
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Convergence of probability measures
P. Billingsley · 1999
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Scaling limits of loop-erased random walks and uniform spanning trees
O. Schramm · 2000
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Values of Brownian intersection exponents. I. Half-plane exponents
G. F. Lawler, O. Schramm, and W. Werner · 2001
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Critical percolation in the plane: conformal invariance, Cardy’s formula, scaling limits
S. Smirnov · 2001
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Conformal invariance of planar loop-erased random walks and uniform spanning trees
G. F. Lawler, O. Schramm, and W. Werner · 2004
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Conformally invariant processes in the plane
G. F. Lawler · 2005
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Basic properties of SLE
S. Rohde and O. Schramm · 2005
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Harmonic explorer and its convergence to SLE 4 {\rm SLE}_{4}
O. Schramm and S. Sheffield · 2005
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Critical percolation and conformal invariance
S. Smirnov · 2005
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Two-dimensional critical percolation: the full scaling limit
F. Camia and C. M. Newman · 2006
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The random-cluster model
G. Grimmett · 2006
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Towards conformal invariance of 2D lattice models
S. Smirnov · 2006
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Critical percolation exploration path and SLE 6 {\rm SLE}_{6} : a proof of convergence
Off-critical lattice models and massive SLEs
N. Makarov and S. Smirnov · 2010
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Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model
S. Smirnov · 2010
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The self-dual point of the two-dimensional random-cluster model is critical for q ≥ 1 q\geq 1
V. Beffara and H. Duminil-Copin · 2012
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Robust Discrete Complex Analysis: A Toolbox
D. Chelkak · 2012
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Universality in the 2D Ising model and conformal invariance of fermionic observables
D. Chelkak and S. Smirnov · 2012
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Strong path convergence from Loewner driving function convergence
S. Sheffield and N. Sun · 2012
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F. Camia and C. M. Newman · 2007
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The scaling limits of planar LERW in finitely connected domains
D. Zhan · 2008
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Contour lines of the two-dimensional discrete Gaussian free field
O. Schramm and S. Sheffield · 2009
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Exploration trees and conformal loop ensembles
S. Sheffield · 2009
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Critical percolation in the plane (long version)
S. Smirnov · 2009
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Probability on graphs
G. Grimmett · 2010
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Crossing probabilities in topological rectangles for the critical planar FK-Ising model
D. Chelkak, H. Duminil-Copin, and C. Hongler · 2013
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Convergence of Ising interfaces to Schramm’s SLE curves
D. Chelkak, H. Duminil-Copin, C. Hongler, A. Kemppainen, and S. Smirnov · 2014
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Continuity of the phase transition for planar Potts models with 1 ≤ q ≤ 4 1\leq q\leq 4
H. Duminil-Copin, V. Sidoravicius, and V. Tassion · 2014
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On the continuity of SLE κ \text{SLE}_{\kappa} in κ \kappa
F. Johansson Viklund, S. Rohde, and C. Wong · 2014
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On convergence of uniform spanning tree interface to SLE(8)
A. Kemppainen · 2015
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Conformal invariance in random cluster models. II. Full scaling limit as a branching SLE
A. Kemppainen and S. Smirnov · 2015
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