Hausdorff dimension of the SLE curve intersected with the real line
arXiv:0711.4070
Abstract
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.
24 pages, 9 figures