Mathematics – Probability
Scientific paper
Jan 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...281..301c&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 281, no. 2, p. 301-313
Mathematics
Probability
69
Astronomical Models, Big Bang Cosmology, Dark Matter, Finite Volume Method, Galactic Clusters, Galactic Evolution, Probability Density Functions, Statistical Correlation, Universe, Computerized Simulation, Error Analysis, Error Correcting Codes, Gravitational Effects, Power Series
Scientific paper
We study finite volume effects on the count probability distribution function PN(l) and the averaged Q-body correlations Xi-barQ (2 less than or = Q less than or equal 5). These statistics are computed for cubic cells, of size l. We use as an example the case of the matter distribution of a cold dark matter (CDM) universe involving approximately 3 x 105 particles. The main effect of the finiteness of the sampled volume is to induce an abrupt cut-off on the function PN(l) at large N. This clear signature makes an analysis of the consequences easy, and one can envisage a correction procedure. As a matter of fact, we demonstrate how an unfair sample can strongly affect the estimates of the functions Xi-barQ for Q greater than or = 3 (and decrease the measured zero of the two-body correlation function). We propose a method to correct for this are fact, or at least to evaluate the corresponding errors. We show that the correlations are systematically underestimated by direct measurements. We find that, once corrected, the statistical properties of the CDM universe appear compatible with the scaling relation SQ identically equals Xi-bar2 exp Q-1 = constant with respect to scale, in the non-linear regime; it was not the case with direct measurments. However, we note a deviation from scaling at scales close to the correlation length. It is probably due to the transition between the highly non-linear regime and the weakly correlated regime, where the functions SQ also seem to present a plateau. We apply the same procedure to simulations with hot dark matter (HDM) and white noise initial conditions, with similar results. Our method thus provides the first accurate measurement of the normalized skewness, S3, and the normalized kurtosis, S4, for three typical models of large scale structure formation in an expanding universe.
Bouchet Francois R.
Colombi Stephane
Schaeffer Richard
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