**4.4. Cluster Abundance and Correlations**

If clusters can be modeled (*e.g.*, using an improved version of
the Press-Schechter formalism) as ``objects'' above a mass threshold in
a density fluctuation field that was initially Gaussian, then
the cluster mass function can be used to constrain
_{8}
_{m}^{0.6}
[49].
The correlation amplitude of these clusters can be compared with their
abundance to give a direct measure of
_{8}.
Together, these results yield
_{m}
and _{8} separately
[50].

*Pro:*
The two parameters are determined from observational data that
are relatively easy to obtain.
The method depends sensitively only on the
assumptions of Gaussian statistics and of mass-limited cluster definition.
It is insensitive to the actual power spectrum of fluctuations.

*Con:*
The amplitude of cluster correlations still carries a large uncertainty.
The method relies on the assumption of Gaussian initial conditions.

*Current Results:*
_{8}
_{m}^{0.6}
0.5 - 0.6
[49]
from cluster abundances (compare to Section 4.1),
but measures of the cluster autocorrelation strength are still too uncertain
to be able to give a useful second constraint
[50].