Moments of the counts distribution in the 1.2 Jy IRAS galaxy redshift survey

Mathematics – Probability

Scientific paper

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Scientific paper

We have measured the count probability distribution in a series of 10 volume-limited sub-samples of a new deep redshift survey of IRAS galaxies. We study the first few moments of this distribution, namely its variance, skewness, and kurtosis, and find remarkably tight relationships to hold between them. In particular the ratio of moments S_3 equiv / ^2 varies at most weakly with scale. On small scales, this is consistent with previous determinations of the three-point correlation function zeta. On larger scales, this conforms with the hypothesis of the growth of the observed structures by gravitational clustering of initially Gaussian density fluctuation. We also show that the various void probability measurements define with great precision a unique function, when rescaled according to the scale-invariance hypothesis (in which the N-point correlation function behaves as a product of N-1 two-point correlation functions).

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