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Biasing in Gaussian Random Fields and Galaxy Correlations.

Gabrielli, Labini, Durrer

    The Astrophysical Journal
    |February 16, 2000
    PubMed
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    Biasing does not alter correlation length in Gaussian random fields. Increasing sparseness of peaks over threshold explains amplified correlation functions, clarifying a literature misconception. This effect does not explain galaxy luminosity or cluster richness correlations.

    Area of Science:

    • Cosmology
    • Statistical Physics
    • Astrophysics

    Background:

    • Gaussian random fields are fundamental models in cosmology and statistical physics.
    • Biasing is a common technique used to study structure formation and galaxy populations.
    • The relationship between correlation length and biasing has been a subject of debate.

    Purpose of the Study:

    • To investigate the effect of biasing on the correlation length in Gaussian random fields.
    • To clarify the interpretation of amplified correlation functions in biased subsets.
    • To determine if peak sparseness explains observed correlation function amplitudes in luminous galaxies and rich clusters.

    Main Methods:

    • Analysis of correlation functions in Gaussian random fields.
    • Interpretation of correlation function amplification based on peak sparseness.

    Related Experiment Videos

  • Comparison of theoretical predictions with observational data for galaxy and cluster correlations.

    • Main Results:

    • Correlation length in a Gaussian random field remains unchanged with biasing.
    • Amplification of correlation functions in biased subsets is attributed to increasing peak sparseness.
    • This sparseness effect does not account for the observed increase in correlation function amplitude with galaxy luminosity or cluster richness.

    Conclusions:

    • Biasing does not alter the intrinsic correlation length of structures in Gaussian random fields.
    • The observed amplification of correlation functions is a consequence of the underlying field's statistical properties (peak sparseness).
    • A long-standing misconception regarding biasing and correlation functions is resolved, with implications for cosmological structure analysis.