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arXiv · 1501.02108

Signal from noise retrieval from one and two-point Green's function - comparison

Zbigniew Drogosz·Jerzy Jurkiewicz·Grzegorz Łukaszewski·Maciej A. Nowak
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Abstract

We compare two methods of eigen-inference from large sets of data, based on the analysis of one-point and two-point Green's functions, respectively. Our analysis points at the superiority of eigen-inference based on one-point Green's function. First, the applied by us method based on Pad?e approximants is orders of magnitude faster comparing to the eigen-inference based on uctuations (two-point Green's functions). Second, we have identified the source of potential instability of the two-point Green's function method, as arising from the spurious zero and negative modes of the estimator for a variance operator of the certain multidimensional Gaussian distribution, inherent for the two-point Green's function eigen-inference method. Third, we have presented the cases of eigen-inference based on negative spectral moments, for strictly positive spectra. Finally, we have compared the cases of eigen-inference of real-valued and complex-valued correlated Wishart distributions, reinforcing our conclusions on an advantage of the one-point Green's function method.

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Zbigniew Drogosz, Jerzy Jurkiewicz, Grzegorz Łukaszewski, Maciej A. Nowak. 2015-01-09. Signal from noise retrieval from one and two-point Green's function - comparison. https://doi.org/10.1103/physreve.92.022111

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