  One possible way to investigate the nature of the primordial power spectrum
fluctuations is by investigating the statistical properties of the local
maximum in the density fluctuation fields. In this work we present a study of
the mean correlation function, $\xi_r$, and the correlation function for high
amplitude fluctuations (the peak-peak correlation) in a slighlty non-Gaussian
context. From the definition of the correlation excess, we compute the Gaussian
two-point correlation function and, using an expansion in Generalized Hermite
polynomials, we estimate the correlation of high density peaks in a
non-Gaussian field with generic distribution and power spectrum. We also apply
the results obtained to a scale-mixed distribution model, which correspond to a
nearly Gaussian model. The results reveal that, even for a small deviation from
Gaussianity, we can expect high density peaks to be much more correlated than
in a Gaussian field with the same power spectrum. In addition, the calculations
reveal how the amplitude of the peaks in the fluctuations field is related to
the existing correlations. Our results may be used as an additional tool to
investigate the behavior of the N-point correlation function, to understand how
non-Gaussian correlations affect the peak-peak statistics and extract more
information about the statistics of the density field.

Astrophysics