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Hausdorff dimensions for SLE$$_6$$. (English) Zbl 1055.60036
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 G. F. Lawler, O. Schramm and 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.

##### MSC:
 60G17 Sample path properties 28A80 Fractals 60J55 Local time and additive functionals 60K35 Interacting random processes; statistical mechanics type models; percolation theory
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##### References:
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