Biasing in Gaussian random fields and galaxy correlations

Abstract

In this letter we show that in a Gaussian random field the correlation length, the typical size of correlated structures, does not change with biasing. We interpret the amplification of the correlation functions of subsets identified by different thresholds being due to the increasing sparseness of peaks over threshold. This clarifies an long-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.Comment: 16 pages, 3 figures, minor changes and corrected some typos to match the version in Astrophysical Journal Letters (2000