High Order Correction Terms for The Peak - Peak Correlation Function in Nearly - Gaussian Models

Context. 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. Aims. In this work we present a study of the mean correlation function, ξ r , and the correlation function for high amplitude fluctuations (peak-peak correlation) in a slighlty non-Gaussian context. Methods. 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. Results. 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. Conclusions. 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.