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We revisit the convergence of loop-erased random walk, LERW, to SLE(2) when the curves are parametrized by capacity.
Gregory F. Lawler, Scott Sheffield, A natural parametrization for the Schramm-Loewner evolution Ann. Probab. Volume 39, Number 5 (2011), 1896-1937
1937
Earlier work this paper cites.
S. E. Warschawsi, On the degree of variation in conformal mapping of variable regions , Trans. AMS, 69(2), 335–356 (1950)
1950
Earlier work this paper cites.
Oded Schramm, Scaling limits of loop-erased walks and uniform spanning trees , Israel J. Math. 118(1) 221-288 (2000)
2000
Earlier work this paper cites.
Gregory F. Lawler, Oded Schramm, Wendelin Werner, Conformal invariance of planar loop-erased random walks and uniform spanning trees , Ann. Probab. Volume 32, Number 1B (2004), 939–995
2004
Earlier work this paper cites.
Michael J. Kozdron and Gregory F. Lawler, Estimates of random walk exit probabilities and applications to loop-erased random walk, Electr. J. Probab. (2005), Paper no. 44, 1442–1467
2005
Earlier work this paper cites.
Steffen Rohde, Oded Schramm, Basic Properties of SLE , Ann. Math., 161
2005
Earlier work this paper cites.
Oded Schramm, David B. Wilson, SLE coordinate changes , New York Journal of Mathematics 11, 659-669 (2005)
2005
Earlier work this paper cites.
Gregory F. Lawler, Conformally Invariant Processes in the Plane
2006
Earlier work this paper cites.
Dapeng Zhan, The scaling limits of planar LERW in finitely connected domains , Ann. Probab., 36(2):467-529, 2008
2008
Cited alongside, same era.
Robert Masson, The growth exponent for planar loop-erased random walk , Electron. j. Prob. 14
2009
Cited alongside, same era.
Gregory F. Lawler, Vlada Limic, Random Walk: a Modern Introduction
2010
Cited alongside, same era.
Fredrik Johansson Viklund, Gregory F. Lawler, Optimal Hölder exponent for the SLE path , Duke Math. J., 159, No. 3, 351–383 (2011)
2011
Cited alongside, same era.
Fredrik Johansson Viklund, Gregory F. Lawler, Almost sure multifractal spectrum for the tip of an SLE curve , Acta Math. 209, 265-322 (2012)
2012
Cited alongside, same era.
Fredrik Johansson Viklund, Steffen Rohde, Carto Wong On the continuity of SLE κ
2014
Later among the works it cites.
Stephane Benoist, Laure Dumaz, Wendelin Werner, Near-critical spanning forests and renormalization , Preprint 2015
2015
Later among the works it cites.
Fredrik Johansson Viklund, Convergence rates for loop-erased random walk and other Loewner curves , Annals of Probability, 43 (1), 119-165 (2015)
2015
Later among the works it cites.
Gregory F. Lawler, Laurence Field, Escape probability and transience for SLE , Electronic Journal of Probability 20 (2015), no. 10, 1-14,
2015
Later among the works it cites.
Gregory F. Lawler, Mohammad A. Rezaei, Minkowski content and natural parameterization for the Schramm-Loewner evolution , Ann. Probab. Volume 43, Number 3 (2015), 1082-1120
2015
Later among the works it cites.
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Christian Beneš, Fredrik Johansson Viklund, Michael Kozdron, On the rate of conference of loop-erased random walk to SLE 2 , Comm. Math. Phys, 308 (2), 307-354 (2013)
2013
Cited alongside, same era.
Gregory F. Lawler, Wang Zhou, SLE curves and natural parametrization , Ann. Probab, Volue 41 Number 3A (2013), 1556–1584
2013
Cited alongside, same era.
Martin Barlow, David Croydon, Takashi Kumagai, Subsequential scaling limits of simple random walk on the two-dimensional uniform spanning tree , To appear in Annals of Probability
Cited in the paper.
Gregory F. Lawler, Continuity of radial and two-sided radial SLE at the terminal point
Cited in the paper.
Christian Beneš, Gregory Lawler, Fredrik Viklund, Scaling limit of the loop-erased random walk Green’s function , Probab. Theory Related Fields, 166 (1), 271-319 (2016)
2016
Closest in time.
Gregory F. Lawler, Fredrik Viklund, Convergence of loop-erased random walk in the natural parametrization , preprint 2016
2016
Closest in time.