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We give a new proof of a result of Kenyon that the growth exponent for loop-erased random walks in two dimensions is 5/4.
A self-avoiding random walk
Gregory F. Lawler · 1980
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Hitting probabilities of random walks on 𝐙 d {\bf Z}^{d}
Harry Kesten · 1987
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Intersections of random walks
Gregory F. Lawler · 1991
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The logarithmic correction for loop-erased walk in four dimensions
Gregory F. Lawler · 1995
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Hausdorff dimension of cut points for Brownian motion
Gregory F. Lawler · 1996
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Generating random spanning trees more quickly than the cover time
David Bruce Wilson · 1996
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The abelian sandpile and related models
Deepak Dhar · 1999
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Loop-erased random walk
Gregory F. Lawler · 1999
Earlier work this paper cites.
The asymptotic determinant of the discrete Laplacian
Richard Kenyon · 2000
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The intersection exponent for simple random walk
Gregory F. Lawler and Emily E. Puckette · 2000
Cited alongside, same era.
Scaling limits of loop-erased random walks and uniform spanning trees
Oded Schramm · 2000
Cited alongside, same era.
Distribution of sizes of erased loops of loop-erased random walks in two and three dimensions
Himanshu Agrawal and Deepak Dhar · 2001
Cited alongside, same era.
Values of Brownian intersection exponents. II. Plane exponents
Gregory F. Lawler, Oded Schramm, and Wendelin Werner · 2001
Cited alongside, same era.
Critical percolation in the plane: conformal invariance, Cardy’s formula, scaling limits
Stanislav Smirnov · 2001
Cited alongside, same era.
Critical exponents for two-dimensional percolation
Stanislav Smirnov and Wendelin Werner · 2001
Cited alongside, same era.
On the scaling limit of planar self-avoiding walk
Gregory F. Lawler, Oded Schramm, and Wendelin Werner · 2004
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Random planar curves and Schramm-Loewner evolutions
Wendelin Werner · 2004
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Conformally invariant processes in the plane
Gregory F. Lawler · 2005
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Basic properties of SLE
Steffen Rohde and Oded Schramm · 2005
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Harmonic explorer and its convergence to SLE 4 {\rm SLE}_{4}
Oded Schramm and Scott Sheffield · 2005
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Two-dimensional critical percolation: the full scaling limit
Federico Camia and Charles M. Newman · 2006
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One-arm exponent for critical 2D percolation
Gregory F. Lawler, Oded Schramm, and Wendelin Werner · 2002
Cited alongside, same era.
The Beurling estimate for a class of random walks
Gregory F. Lawler and Vlada Limic · 2004
Cited alongside, same era.
Conformal invariance of planar loop-erased random walks and uniform spanning trees
Gregory F. Lawler, Oded Schramm, and Wendelin Werner · 2004
Cited alongside, same era.
Second moment estimates for loop-erased random walk
Martin Barlow and Robert Masson
Cited in the paper.
Random walk: a modern introduction
Gregory F. Lawler and Vlada Limic
Cited in the paper.
Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model
Stanislav Smirnov
Cited in the paper.
Oded Schramm and Scott Sheffield · 2006
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Critical percolation exploration path and SLE 6 {\rm SLE}_{6} : a proof of convergence
Federico Camia and Charles M. Newman · 2007
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The dimension of the SLE curves
Vincent Beffara · 2008
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