arXiv subjects

Stéphane Colombi

Publications and source records attributed to Stéphane Colombi.

21 records · Page 2Linked to original sources

arXiv1999

Experimental Cosmic Statistics I: Variance

Counts-in-cells are measured in the $τ$CDM Virgo Hubble Volume simulation. This large N-body experiment has 10^9 particles in a cubic box of size 2000 h^{-1} Mpc. The unprecedented combination of size and resolution allows for the first time a realistic numerical analysis of the cosmic errors and cosmic correlations of statistics related to counts-in-cells measurements, such as the probability distribution function P_N itself, its factorial moments F_k and the related cumulants $\xiav$ and S_N's. These statistics are extracted from the whole simulation cube, as well as from 4096 sub-cubes of size 125 h^{-1}Mpc, each representing a virtual random realization of the local universe. The measurements and their scatter over the sub-volumes are compared to the theoretical predictions of Colombi, Bouchet & Schaeffer (1995) for P_0, and of Szapudi & Colombi (1996, SC) and Szapudi, Colombi & Bernardeau (1999a, SCB) for the factorial moments and the cumulants. The general behavior of experimental variance and cross-correlations as functions of scale and order is well described by theoretical predictions, with a few percent accuracy in the weakly non-linear regime for the cosmic error on factorial moments. (... more in paper >...)

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arXiv1999

Experimental Cosmic Statistics II: Distribution

Colombi et al. 1999 (paper I) investigated the counts-in-cells statistics and their respective errors in the $τ$CDM Virgo Hubble Volume simulation. This extremely large $N$-body experiment also allows a numerical investigation of the {\em cosmic distribution function}, $Υ(\tA)$ itself for the first time. For a statistic $A$, $Υ(\tA)$ is the probability density of measuring the value $\tA$ in a finite galaxy catalog. $Υ$ was evaluated for the distribution of counts-in-cells, $P_N$, the factorial moments, $F_k$, and the cumulants, $\xiav$ and $S_N$'s, using the same subsamples as paper I. While paper I concentrated on the first two moments of $Υ$, i.e. the mean, the cosmic error and the cross-correlations, here the function $Υ$ is studied in its full generality, including a preliminary analysis of joint distributions $Υ(\tA,\tB)$. The most significant, and reassuring result for the analyses of future galaxy data is that the cosmic distribution function is nearly Gaussian provided its variance is small. A good practical criterion for the relative cosmic error is that $ΔA/A \la 0.2$. This means that for accurate measurements, the theory of the cosmic errors, presented by Szapudi & Colombi (1996) and Szapudi, Colombi & Bernardeau (1999), and confirmed empirically by paper I, is sufficient for a full statistical description and thus for a maximum likelihood rating of models. As the cosmic error increases, the cosmic distribution function $Υ$ becomes increasingly skewed and is well described by a generalization of the lognormal distribution. The cosmic skewness is introduced as an additional free parameter. (...more in paper...)

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arXiv1995

Cosmic Error and the Statistics of Large Scale Structure

We examine the errors on counts in cells extracted from galaxy surveys. The measurement error, related to the finite number of sampling cells, is disentangled from the ``cosmic error'', due to the finiteness of the survey. Using the hierarchical model and assuming locally Poisson behavior, we identified three contributions to the cosmic error: The finite volume effect is proportional to the average of the two-point correlation function over the whole survey. It accounts for possible fluctuations of the density field at scales larger than the sample size. The edge effect is related to the geometry of the survey. It accounts for the fact that objects near the boundary carry less statistical weight than those further away from it. The discreteness effect is due to the fact that the underlying smooth random field is sampled with finite number of objects. This is the ``shot noise'' error. Measurements of errors in artificial hierarchical samples showed excellent agreement with our predictions. The probability distribution of errors is increasingly skewed when the order $N$ and/or the cell size increases. The Gaussian approximation is valid only in the weakly non-linear regime, otherwise it severely underestimates the true errors. We study the concept of ``number of statistically independent cells'' This number is found to depend highly on the statistical object under study and is generally quite different from the number of cells needed to cover the survey volume. In light of these findings, we advocate high oversampling for measurements of counts in cells.

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