Displaying similar documents to “On the second-order correlation function of the characteristic polynomial of a real symmetric Wigner matrix.”

The rate of convergence for spectra of GUE and LUE matrix ensembles

Friedrich Götze, Alexander Tikhomirov (2005)

Open Mathematics

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We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.

Characteristic polynomials of sample covariance matrices: The non-square case

Holger Kösters (2010)

Open Mathematics

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We consider the sample covariance matrices of large data matrices which have i.i.d. complex matrix entries and which are non-square in the sense that the difference between the number of rows and the number of columns tends to infinity. We show that the second-order correlation function of the characteristic polynomial of the sample covariance matrix is asymptotically given by the sine kernel in the bulk of the spectrum and by the Airy kernel at the edge of the spectrum. Similar results...