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.
Whole-plane self-avoiding walks and radial Schramm-Loewner evolution : a numerical study / M. Gherardi. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 136:5(2009 Sep), pp. 864-874.
Whole-plane self-avoiding walks and radial Schramm-Loewner evolution : a numerical study
M. GherardiPrimo
2009
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.Pubblicazioni consigliate
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