Correlations of peaks of Gaussian random fields

The high peaks of a Gaussian random field are studied. Asymptotic expansions, appropriate for high peak thresholds and large spatial separations, are developed for the N-point correlation functions of the number density of high peaks, in terms of the two-point correlation of the underlying Gaussian field. Similar expressions are derived for the correlations of points, not necessarily the positions of peaks, where the field exceeds a high threshold