Communications in Mathematical Physics

, Volume 318, Issue 2, pp 307–354 | Cite as

On the Rate of Convergence of Loop-Erased Random Walk to SLE2

  • Christian Beneš
  • Fredrik Johansson Viklund
  • Michael J. Kozdron


We derive a rate of convergence of the Loewner driving function for a planar loop-erased random walk to Brownian motion with speed 2 on the unit circle, the Loewner driving function for radial SLE2. The proof uses a new estimate of the difference between the discrete and continuous Green’s functions that is an improvement over existing results for the class of domains we consider. Using the rate for the driving process convergence along with additional information about SLE2, we also obtain a rate of convergence for the paths with respect to the Hausdorff distance.


Random Walk Simple Random Walk Grid Domain Loewner Chain Loewner Equation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Christian Beneš
    • 1
  • Fredrik Johansson Viklund
    • 2
  • Michael J. Kozdron
    • 3
  1. 1.Department of MathematicsBrooklyn College of the City University of New YorkBrooklynUSA
  2. 2.Department of MathematicsColumbia UniversityNew YorkUSA
  3. 3.Department of Mathematics & StatisticsUniversity of ReginaReginaCanada

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