  A highly non-gaussian cosmological perturbation with a flat spectrum has
unusual stochastic properties. We show that they depend on the size of the box
within which the perturbation is defined, but that for a typical observer the
parameters defining the perturbation `run' to compensate for any change in the
box size. Focusing on the primordial curvature perturbation, we show that an
un-correlated gaussian-squared component is bounded at around the 10% level by
the WMAP bound on the bispectrum, and we show that a competitive bound may
follow from the trispectrum when it too is bounded by WMAP. Similar
considerations apply to a highly non-gaussian isocurvature perturbation.
