Biasing in Gaussian random fields and galaxy correlations

In this Letter, we show that in a Gaussian random field, the correlation le ngth-the typical size of correlated structures-does not change with biasing . We interpret the amplification of the correlation functions of subsets id entified by different thresholds as being caused by the increasing sparsene ss of peaks over threshold. This clarifies a long-standing misconception in the literature. We also argue that this effect does not explain the observ ed increase of the amplitude of the correlation function xi(r) when galaxie s of brighter luminosity or galaxy clusters of increasing richness are cons idered.