Whole-plane self-avoiding walks and radial Schramm-Loewner evolution: a numerical study

Details Whole-plane self-avoiding walks and radial Schramm-Loewner evolution: a numerical study Whole-plane self-avoiding walks and radial Schramm-Loewner evolution: a numerical study

2009-03-20

arxiv.org/abs/0903.3503v1

J. Stat. Phys. (2009) 136:864-874

Physics

Condensed Matter

Statistical Mechanics

15 pages, 4 figures

Scientific paper

We numerically test the correspondence between the scaling limit of self-avoiding walks (SAW) in the plane and Schramm-Loewner evolution (SLE) with k=8/3. We introduce a discrete-time process approximating SLE in the exterior of the unit 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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