In this talk I review the main characteristics of the large-scale structure of the universe traced by
the distribution of the galaxies.
Second-order functions such as the two-point correlation function or the power spectrum are described, and recent results on the application of these statistical measures on the new redshift surveys are reviewed. It is shown how these statistics are blind to detect the morphology of the galaxy distribution and therefore, other descriptors such as higher order correlation functions or morphological measures are needed to fully characterize the large scale structure.
The use of Minkowski functionals for this purpose is illustrated. Its dependence on the smoothing method
is then analyzed and a consistent method to estimate the density field from a point process based on the "a trous"
wavelet is introduced. The goal is to recover the underlying topology of the point distribution measured by the Euler-Poincare characteristic by applying it to the unique reconstruction of the density field provided by the wavelet denoising method.
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