  Poisson distributed shot noise is normally considered in the Gaussian limit
in cosmology. However, if the shot noise is large enough and the correlation
function/power spectrum conspires, the Gaussian approximation mis-estimates the
errors and their covariance significantly. The power spectrum, even for
initially Gaussian densities,acquires cross correlations which can be large,
while the change in the correlation function error matrix is diagonal except at
zero separation. Two and three dimensional power law correlation function and
power spectrum examples are given. These corrections appear to have a large
effect when applied to galaxy clusters, e.g. for SZ selected galaxy clusters in
2 dimensions. This can increase the error estimates for cosmological parameter
estimation and consequently affect survey strategies, as the corrections are
minimized for surveys which are deep and narrow rather than wide and shallow.
In addition, a rewriting of the error matrix for the power spectrum/correlation
function is given which eliminates most of the Bessel function dependence (in
two dimensions) and all of it (in three dimensions), which makes the
calculation of the error matrix more tractable. This applies even when the shot
noise is in the (usual) Gaussian limit.
