Biasing in Gaussian random fields and galaxy correlations

In this letter we show that in a Gaussian random field with density-density correlations the typical dimension of structures formed by fluctuations does not change with biasing. We clarify how the amplification of the correlation functions of subsets of points identified by different thresholds is due to a particular increase of the sparseness of peaks over threshold itself. 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 $\xi(r)$ when galaxies of brighter luminosity or galaxy clusters of increasing richness are considered.