  We probe the statistical nature of the primordial density field by measuring
correlations between the power in adjacent Fourier modes. For certain types of
non-Gaussian field, these k-space correlations would be expected to be more
extended than for a Gaussian field, providing a useful discriminatory test for
Gaussian fields. We apply this test to the combined QDOT and 1.2-Jy IRAS galaxy
survey and find the observed density field to be in good agreement with having
Gaussian density fluctuations for modes with k < 0.1 h/Mpc. From this result we
are able to set quantitative limits on a class of possible non-Gaussian
distributions -- the product of a Gaussian field with an independent stochastic
field. The maximum sensitivity is to modulations of a Gaussian field with
coherence scales of 30 Mpc/h and the rms modulation on this scale cannot
greatly exceed unity. We discuss the improvements to this limit likely to be
set by future surveys.
