  Stationary wave functions at the transition between plateaus of the integer
quantum Hall effect are known to exhibit multi-fractal statistics. Here we
explore this critical behavior for the case of scattering states of the
Chalker-Coddington model with point contacts. We argue that moments formed from
the wave amplitudes of critical scattering states decay as pure powers of the
distance between the points of contact and observation. These moments in the
continuum limit are proposed to be correlations functions of primary fields of
an underlying conformal field theory. We check this proposal numerically by
finite-size scaling. We also verify the CFT prediction for a 3-point function
involving two primary fields.
