Hausdorff dimensions for SLE6
Copyright policy )Hausdorff dimensions for SLE6
We prove that the Hausdorff dimension of the trace of SLE_6 is almost surely 7/4 and give a more direct derivation of the result (due to Lawler-Schramm-Werner) that the dimension of its boundary is 4/3. We also prove that, for all κ<8, the SLE_κ trace has cut-points.
Published at http://dx.doi.org/10.1214/009117904000000072 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], 60D05, 60G17, 28A80. (Primary), 28A80, Mathematics - Complex Variables, Probability (math.PR), SLE, Interacting random processes; statistical mechanics type models; percolation theory, Hausdorff dimension, Local time and additive functionals, stochastic Loewner evolution, Fractals, cut-point, 60G17, FOS: Mathematics, Sample path properties, 60D05, Brownian motion, Complex Variables (math.CV), Mathematics - Probability
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], 60D05, 60G17, 28A80. (Primary), 28A80, Mathematics - Complex Variables, Probability (math.PR), SLE, Interacting random processes; statistical mechanics type models; percolation theory, Hausdorff dimension, Local time and additive functionals, stochastic Loewner evolution, Fractals, cut-point, 60G17, FOS: Mathematics, Sample path properties, 60D05, Brownian motion, Complex Variables (math.CV), Mathematics - Probability
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