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It is of fundamental importance to determine if and how hierarchical clustering is involved in large-scale structure formation of the universe. Hierarchical evolution is characterized by rules which specify how dark matter halos are formed by the merging of halos at smaller scales. We show that scale-scale correlations of the matter density field are direct and sensitive measures to quantify this merging tree. Such correlations are most conveniently determined from discrete wavelet transforms. Analyzing two samples of Ly-alpha forests of QSOs absorption spectra, we find significant scale-scale correlations whose dependence is typical for a branching process. Therefore, models which predict a history independent evolution are ruled out and the halos hosting the Ly-alpha clouds must have gone through a history dependent merging process during their formation.
We present a detailed review of large-scale structure (LSS) study using the discrete wavelet transform (DWT). After describing how one constructs a wavelet decomposition we show how this bases can be used as a complete statistical discription of LSS.
We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non--linear filter with Gaussian input. The wavelet coefficients that appear in
We propose a large-scale hologram calculation using WAvelet ShrinkAge-Based superpositIon (WASABI), a wavelet transform-based algorithm. An image-type hologram calculated using the WASABI method is printed on a glass substrate with the resolution of
We show that scale-scale correlations are a generic feature of slow-roll inflation theories. These correlations result from the long-time tails characteristic of the time dependent correlations because the long wavelength density perturbation modes a
We generalize the stochastic theory of hierarchical clustering presented in paper I by Lapi & Danese (2020) to derive the (conditional) halo progenitor mass function and the related large-scale bias. Specifically, we present a stochastic differential