Biasing in Gaussian Random Fields and Galaxy Correlations

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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 as being caused by the increasing sparseness of peaks over threshold. This clarifies a 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 ξ(r) when galaxies of brighter luminosity or galaxy clusters of increasing richness are considered.

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