Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices

article Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices published yes Giorgio Cipolloni author 42198EFA-F248-11E8-B48F-1D18A9856A870000-0002-4901-7992 László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 LaEr department Random matrices, universality and disordered quantum systems project International IST Doctoral Program project We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W˜ and its minor W. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of W˜ and W. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish. World Scientific Publishing2020 eng Random Matrices: Theory and Application 2010-3263 2010-3271 1806.08751 00054746440000110.1142/S2010326320500069 93 G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” Random Matrices: Theory and Application, vol. 9, no. 3. World Scientific Publishing, 2020. Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 9(3), 2050006. Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application. World Scientific Publishing, 2020. <a href="https://doi.org/10.1142/S2010326320500069">https://doi.org/10.1142/S2010326320500069</a>. Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 2020;9(3). doi:<a href="https://doi.org/10.1142/S2010326320500069">10.1142/S2010326320500069</a> Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020, doi:<a href="https://doi.org/10.1142/S2010326320500069">10.1142/S2010326320500069</a>. G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020). Cipolloni, G., & Erdös, L. (2020). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. World Scientific Publishing. <a href="https://doi.org/10.1142/S2010326320500069">https://doi.org/10.1142/S2010326320500069</a> 64882019-05-26T21:59:14Z2025-07-10T11:53:26Z