Hausdorff dimension of the SLE curve intersected with the real line

Details Hausdorff dimension of the SLE curve intersected with the real line Hausdorff dimension of the SLE curve intersected with the real line

2007-11-26

arxiv.org/abs/0711.4070v1

Electron. Jour. Probab., 13:1166-1188 (electronic), 2008

Mathematics

Probability

24 pages, 9 figures

Scientific paper

We establish an upper bound on the asymptotic probability of an SLE(kappa)
curve hitting two small intervals on the real line as the interval width goes
to zero, for the range 4 < kappa < 8. As a consequence we are able to prove
that the SLE curve intersected with the real line has Hausdorff dimension
2-8/kappa, almost surely.

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