Hausdorff dimensions for SLE\(_6\). (Q1889793)

The author proves that the Hausdorff dimension of the trace of SLE\(_6\) is almost surely \(7/4\) and the dimension of its trace is \(4/3\). Using this, he gives a more direct deviation of the result of \textit{G. F. Lawler, O. Schramm} and \textit{W. Werner} [Math. Res. Lett. 8, No. 1--2, 13--23 (2001; Zbl 0993.60085)] that the dimension of the planar Brownian frontier is \(4/3\). The author also proves that, for all \(\kappa<8\), the SLE\(_\kappa\) trace has cut-points.