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arXiv · 1206.1956

On the Continuity of SLE(κ) in κ

Fredrik Johansson Viklund·Steffen Rohde·Carto Wong
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Abstract

We prove that for almost every Brownian motion sample, the corresponding SLE(κ) curves parameterized by capacity exist and change continuously in the supremum norm when κvaries in the interval [0,κ_0), where κ_0=8(2-\sqrt{3})=2.143... We estimate the κ-dependent modulus of continuity of the curves and also give an estimate on the modulus of continuity for the supremum norm change with κ.

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Fredrik Johansson Viklund, Steffen Rohde, Carto Wong. 2012-06-09. On the Continuity of SLE(κ) in κ. https://arxiv.org/abs/1206.1956

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