1997/01/29 by Li‐Zhi Fang, Fang, Li-Zhi, Jesús Pando +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Astrophysics (astro-ph) #Calibration and Measurement Techniques #FOS: Physical sciences #Scientific Research and Discoveries #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.astro-ph/9701228
openalex publication_date 1997/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. Among the topics studied are the the DWT estimation of the probability distribution function; the reconstruction of the power spectrum; the regularization of complex geometry in observational samples; cluster identification; extraction and identification of coherent structures; scale-decomposition of non-Gaussianity, such as spectra of skewnes and kurtosis and scale-scale correlations. These methods are applied to both observational and simulated samples of the QSO Lyman-alpha forests. It is clearly demonstrated that the statistical measures developed using the DWT are needed to distinguish between competing models of structure formation. The DWT also reveals physical features in these distributions not detected before. We conclude with a look towards the future of the use of the DWT in LSS.