Much of the dynamical behavior concerning the large scale structure
formation of the universe is only revealed when statistical properties
of the relevant cosmic random fields are studied in phase
(position-scale) space. The discrete wavelet transformation (DWT)
decomposition provides a powerful tool to describe highly nonlinear
clustering in which correlations in both position and scale space must
be treated simultaneously. The DWT has been shown to be especially
effective in testing dynamical models with their predictions
of the phase space features of the cosmic fields. I will briefly
report some these results. These include 1.) phenomenological
hierarchical clustering models and scale-scale correlations; 2.) the
LCDM model and intermittency; 3.) the Gaussianity of initial
perturbations and quasi-locality of the DWT mode-mode correlations.
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