0000000000281906
AUTHOR
María-jesús Pons-bordería
showing 4 related works from this author
Comparing estimators of the galaxy correlation function
1999
We present a systematic comparison of some usual estimators of the 2--point correlation function, some of them currently used in Cosmology, others extensively employed in the field of the statistical analysis of point processes. At small scales, it is known that the correlation function follows reasonably well a power--law expression $\xi(r) \propto r^{-\gamma}$. The accurate determination of the exponent $\gamma$ (the order of the pole) depends on the estimator used for $\xi(r)$; on the other hand, its behavior at large scale gives information on a possible trend to homogeneity. We study the concept, the possible bias, the dependence on random samples and the errors of each estimator. Erro…
Does the galaxy correlation length increase with the sample depth?
2001
We have analyzed the behavior of the correlation length, $r_0$, as a function of the sample depth by extracting from the CfA2 redshift survey volume--limited samples out to increasing distances. For a fractal distribution, the value of $r_0$ would increase with the volume occupied by the sample. We find no linear increase for the CfA2 samples of the sort that would be expected if the Universe preserved its small scale fractal character out to the distances considered (60--100$\hmpc$). The results instead show a roughly constant value for $r_0$ as a function of the size of the sample, with small fluctuations due to local inhomogeneities and luminosity segregation. Thus the fractal picture ca…
Searching for the scale of homogeneity
1998
We introduce a statistical quantity, known as the $K$ function, related to the integral of the two--point correlation function. It gives us straightforward information about the scale where clustering dominates and the scale at which homogeneity is reached. We evaluate the correlation dimension, $D_2$, as the local slope of the log--log plot of the $K$ function. We apply this statistic to several stochastic point fields, to three numerical simulations describing the distribution of clusters and finally to real galaxy redshift surveys. Four different galaxy catalogues have been analysed using this technique: the Center for Astrophysics I, the Perseus--Pisces redshift surveys (these two lying…
The best fit for the observed galaxy Counts-in-Cell distribution function
2017
The Sloan Digital Sky Survey (SDSS) is the first dense redshift survey encompassing a volume large enough to find the best analytic probability density function that fits the galaxy Counts-in-Cells distribution $f_V(N)$, the frequency distribution of galaxy counts in a volume $V$. Different analytic functions have been previously proposed that can account for some of the observed features of the observed frequency counts, but fail to provide an overall good fit to this important statistical descriptor of the galaxy large-scale distribution. Our goal is to find the probability density function that better fits the observed Counts-in-Cells distribution $f_V(N)$. We have made a systematic stud…