Note on the existence and modulus of continuity of the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\textit{SLE}}_8$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi mathvariant="italic">SLE</mi> <mn>8</mn> </msub> </math> </EquationSource> </InlineEquation> curve

We review one method for estimating the modulus of continuity of a Schramm–Loewner evolution (SLE) curve in terms of the inverse Loewner map. Then we prove estimates about the distribution of the inverse Loewner map, which underpin the difficulty in bounding the modulus of continuity of SLE for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\kappa =8$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="italic">κ</mi> <mo>=</mo> <mn>8</mn> </mrow> </math> </EquationSource> </InlineEquation>. The main idea in the proof of these estimates is applying the Girsanov theorem to reduce the problem to estimates about one-dimensional Brownian motion. Copyright Springer-Verlag Berlin Heidelberg 2014