Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices Cipolloni, Giorgio ; https://orcid.org/0000-0002-4901-7992 Erdös, László ; https://orcid.org/0000-0001-5366-9603 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 Publishing 2020 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/6488 Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. <i>Random Matrices: Theory and Application</i>. 2020;9(3). doi:<a href="https://doi.org/10.1142/S2010326320500069">10.1142/S2010326320500069</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1142/S2010326320500069 info:eu-repo/semantics/altIdentifier/issn/2010-3263 info:eu-repo/semantics/altIdentifier/e-issn/2010-3271 info:eu-repo/semantics/altIdentifier/wos/000547464400001 info:eu-repo/semantics/altIdentifier/arxiv/1806.08751 info:eu-repo/semantics/openAccess