Abstract
We numerically test the correspondence between the scaling limit of self-avoiding walks (SAW) in the plane and Schramm-Loewner evolution (SLE) with κ=8/3. We introduce a discrete-time process approximating SLE in the exterior of a small disc and compare the distribution functions for an internal point in the SAW and a point at a fixed fractal variation on the SLE, finding good agreement. This provides numerical evidence in favor of a conjecture by Lawler, Schramm and Werner. The algorithm turns out to be an efficient way of computing the position of an internal point in the SAW.
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Gherardi, M. Whole-Plane Self-avoiding Walks and Radial Schramm-Loewner Evolution: A Numerical Study. J Stat Phys 136, 864–874 (2009). https://doi.org/10.1007/s10955-009-9797-y
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DOI: https://doi.org/10.1007/s10955-009-9797-y