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arXiv · 1611.01406

The Loewner difference equation and convergence of loop-erased random walk

Gregory F. Lawler·Fredrik Viklund
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Abstract

We revisit the convergence of loop-erased random walk, LERW, to SLE(2) when the curves are parametrized by capacity. We construct a coupling of the chordal version of LERW and chordal SLE(2) based on the Green's function for LERW as martingale observable and using an elementary discrete-time Loewner "difference" equation. This coupling is different than the ones previously considered in this context. Our recent work (arXiv:1603.05203) on the convergence of LERW parametrized by length to SLE(2) parameterized by Minkowski content uses specific features of the coupling constructed here.

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Gregory F. Lawler, Fredrik Viklund. 2016-11-04. The Loewner difference equation and convergence of loop-erased random walk. https://arxiv.org/abs/1611.01406

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