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Whole-Plane Self-avoiding Walks and Radial Schramm-Loewner Evolution: A Numerical Study

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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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  1. Dipartimento di Fisica and INFN, Sezione di Milano, Università degli Studi di Milano, Via Celoria 16, 20133, Milano, Italy

    Marco Gherardi

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  1. Marco Gherardi
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Correspondence to Marco Gherardi.

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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

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