  Gaussian cosmological models, typified by the inflationary cold dark matter
models, and non-Gaussian topological defect based cosmological models, such as
the texture seeded model, differ in the origin of large-scale cosmic
structures. In the former it is believed that peaks at appropriate scales in
the initial high density field are the sites onto which matter accretes and
collapses to form the present galaxies and clusters of galaxies, whereas in the
latter these structures can form around the density perturbation seeds (which
are textures in the texture model). Textures initially are randomly distributed
on scales larger than their size, in sharp contrast to the initial high density
peaks in the Gaussian models which are already strongly clustered before any
gravitational evolution has occured. One thus expects that the resultant
correlation of large cosmic objects such as clusters of galaxies in the texture
model should be significantly weaker than its Gaussian counterpart.
  We show that an $\Omega_0=1$ biased $b=2$ (as required by cluster abundance
observations) texture model (or any random seed model) predicts a two-point
correlation length of $\le 6.0h^{-1}$Mpc for rich clusters, independent of
richness. On the other hand, the observed correlation length for rich clusters
is $\ge 10.0h^{-1}$Mpc at an approximately $2\sigma$ confidence level. It thus
appears that the global texture cosmological model or any random seed
cosmological models of this sort are ruled out at a very high confidence
($>3\sigma$).
