A multifractal SLE_kappa(rho) boundary spectrum

In a recent work, we have derived an almost sure multifractal boundary spectrum for SLE_kappa(rho)-processes. Finding the upper bound on the dimension is fairly standard and is done with the help of Girsanov's theorem. The lower bound on the dimension, however, is a bit more cumbersome. To find this, we use the imaginary geometry coupling of SLE and GFF to find a sufficient two-point estimate. In this talk, we will mainly focus on construction of the perfect points and the method of finding the two-point estimate.