Extension and estimation of correlations in cold dark matter models

discuss the large-scale properties of standard cold dark-matter models characterizing the main features of the power, of the two-point correlation function, and of the mass. Both the real-space statistics show a very well-defined on large enough scales, for their amplitudes to become than unity. The correlation function, in the range0<\ξ(r)<1, is characterized by a typical length scale rc, where\ξ(r\ c)=0, which is fixed by the physics of the early. Beyond this scale it becomes negative, going to zero with a proportional to -(r⁻⁴). These anti-correlations thus an important observational challenge for verifying models in space. The same length scale rc characterizes the behavior of mass variance, which decays for r>r\ c as r-4, the fastest of any mass distribution. The length-scale rc defines the extension of (positively correlated) structures in these. These are the features expected for the dark-matter field: galaxies, which represent a biased field, may differ in their, which we analyze. We then discuss the detectability of real-space features by considering several estimators of the-point correlation function. By making tests on numerical, we emphasize the important role of finite size effects, should always be controlled for careful measurements.