  The harmonic measure (or diffusion field or electrostatic potential) near a
percolation cluster in two dimensions is considered. Its moments, summed over
the accessible external hull, exhibit a multifractal 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 walks or self-avoiding
walks. An exact application to the anomalous impedance of a rough percolative
electrode is given. The numerical checks are excellent. Another set of exact
and universal multifractal exponents is obtained for n independent
self-avoiding walks anchored at the boundary of a percolation cluster. These
exponents describe the multifractal scaling behavior of the average nth moment
of the probabity for a SAW to escape from the random fractal boundary of a
percolation cluster in two dimensions.
