Biasing in Gaussian random fields and galaxy correlations

Abstract

In this letter we show that the peaks of a Gaussian random field, with density-density correlations on small scales, are not more `strongly correlated' than the field itself: they are more sparse. The peaks are (almost) connected regions identified by a certain threshold in the density field, and their spatial extension is of the order of the correlated patches of the original Gaussian field. The amplification of the correlation function of the peaks selected by a certain threshold, usually referred to as `biasing', has nothing to do with how `strongly clustered' the peaks are but is due to their sparseness. This clarifies an old-standing misconception in the literature. We also argue that this effect does not explain the observed increase of the amplitude of the correlation function [...] when galaxies of brighter luminosity or galaxy clusters of increasing richness are considered