Harmonic measure exponents for two-dimensional percolation

The harmonic measure (or diffusion field) near a critical percolation cluster in two dimensions (2D) is considered. Its moments, summed over the accessible external hull, exhibit a multifractal (MF) spectrum, which I calculate exactly. The generalized dimensions D(n) as well as the MF function f(alpha) are derived from generalized conformal invariance, and are shown to be identical to those of the harmonic measure on 2D random or self-avoiding walks. An application to the impedance of a rough percolative electrode is given. The numerical checks are excellent.