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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.