2014/02/26 by G. Torres-Vargas, Rubén Fossión, Vargas, G. Torres +6
Computer Science · Mathematics · Physics and Astronomy · #Blind Source Separation Techniques #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Quantum chaos and dynamical systems #Quantum optics and atomic interactions #Random Matrices and Applications #Scientific Research and Discoveries #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1402.6786
openalex publication_date 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, the singular value decomposition (SVD) was applied to standard\nGaussian ensembles of Random Matrix Theory (RMT) to determine the scale\ninvariance in the spectral fluctuations without performing any unfolding\nprocedure. Here, SVD is applied directly to the \ν-Hermite ensemble and to a\nsparse matrix ensemble, decomposing the corresponding spectra in trend and\nfluctuation modes. In correspondence with known results, we obtain that\nfluctuation modes exhibit a cross-over between soft and rigid behavior. By\nusing the trend modes we performed a data-adaptive unfolding, and we calculate\ntraditional spectral fluctuation measures. Additionally, ensemble-averaged and\nindividual-spectrum averaged statistics are calculated consistently within the\nsame basis of normal modes.\n