On the $\log$-regularity of SLE${}_4$

Abstract

We prove that the welding homeomomorphism of SLE${}_4$ is almost surely $\log$-regular. In a previous version of this work, we had erroneously deduced its removability from this property. Nevertheless, the $\log$-regularity does provide some information and could lead to future developments.

arXiv comment12 pages. Major changes. Due to a mistake in the proof, Theorem 1.1 of the previous version does not hold. This does not affect the part on the $\log$-regularity of SLE${}_4$, but its removability cannot be deduced simply from this property

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