{"issue":"3","abstract":[{"lang":"eng","text":"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."}],"quality_controlled":"1","isi":1,"department":[{"_id":"LaEr"}],"year":"2020","volume":9,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"ec_funded":1,"date_updated":"2023-08-28T08:38:48Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1806.08751"}],"doi":"10.1142/S2010326320500069","citation":{"short":"G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).","ista":"Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 9(3), 2050006.","chicago":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices: Theory and Application</i>. World Scientific Publishing, 2020. <a href=\"https://doi.org/10.1142/S2010326320500069\">https://doi.org/10.1142/S2010326320500069</a>.","mla":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices: Theory and Application</i>, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020, doi:<a href=\"https://doi.org/10.1142/S2010326320500069\">10.1142/S2010326320500069</a>.","apa":"Cipolloni, G., &#38; Erdös, L. (2020). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. <i>Random Matrices: Theory and Application</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S2010326320500069\">https://doi.org/10.1142/S2010326320500069</a>","ieee":"G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” <i>Random Matrices: Theory and Application</i>, vol. 9, no. 3. World Scientific Publishing, 2020.","ama":"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>"},"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"},{"call_identifier":"H2020","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385"}],"article_type":"original","title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","type":"journal_article","intvolume":"         9","author":[{"orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"}],"publisher":"World Scientific Publishing","oa_version":"Preprint","month":"07","publication_identifier":{"issn":["20103263"],"eissn":["20103271"]},"article_number":"2050006","publication_status":"published","date_published":"2020-07-01T00:00:00Z","article_processing_charge":"No","day":"01","status":"public","publication":"Random Matrices: Theory and Application","_id":"6488","scopus_import":"1","date_created":"2019-05-26T21:59:14Z","external_id":{"isi":["000547464400001"],"arxiv":["1806.08751"]},"language":[{"iso":"eng"}]}