Continuous wavelet analysis of matter clustering using the
  Gaussian-derived wavelet
  Continuous wavelet analysis has been increasingly employed in various fields
of science and engineering due to its remarkable ability to maintain optimal
resolution in both space and scale. Here, we introduce wavelet-based
statistics, including the wavelet power spectrum, wavelet cross-correlation and
wavelet bicoherence, to analyze the large-scale clustering of matter. For this
purpose, we perform wavelet transforms on the density distribution obtained
from the one-dimensional Zel'dovich approximation and then measure the wavelet
power spectra and wavelet bicoherences of this density distribution. Our
results suggest that the wavelet power spectrum and wavelet bicoherence can
identify the effects of local environments on the clustering at different
scales. Moreover, we apply the statistics based on the three-dimensional
isotropic wavelet to the IllustrisTNG simulation at z = 0, and investigate the
environmental dependence of the matter clustering. We find that the clustering
strength of the total matter increases with increasing local density except on
the largest scales. Besides, we notice that the gas traces the dark matter
better than stars on large scales in all environments. On small scales, the
cross-correlation between the dark matter and gas first decreases and then
increases with increasing density. This is related to the impacts of the AGN
feedback on the matter distribution, which also varies with the density
environment in a similar trend to the cross-correlation between the dark matter
and gas. Our findings are qualitatively consistent with previous studies about
the matter clustering.
