Statistics of density maxima and the large-scale matter distribution

High peaks in Gaussian noise display enhanced clustering. The enhancement takes two forms: on large scales one obtains a linear amplification of the correlation function which is independent of scale. On smaller scales, but larger than the mass scale of the peaks themselves, a nonlinear (exponential) enhancement of the number density of high peaks in overdense regions arises. The large-scale correlations of Abell's rich clusters can be understood as a manifestation of this phenomenon. If the formation of bright galaxies favors the high overdensity peaks then the number of galaxies (per unit mass) in clusters and groups may be considerably enhanced. Consequences of these ideas for the density parameter and the large-scale matter distribution are discussed.