Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices
2019 ◽
Vol 09
(03)
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pp. 2050006
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Keyword(s):
We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix [Formula: see text] and its minor [Formula: see text]. 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 [Formula: see text] and [Formula: see text]. 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.
2015 ◽
Vol 59
(2)
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pp. 185-207
2017 ◽
Vol 31
(2)
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pp. 1024-1057
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2005 ◽
Vol 58
(10)
◽
pp. 1316-1357
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Keyword(s):
2021 ◽
Vol 57
(1)
◽
2018 ◽
Vol 45
(3)
◽
pp. 699-728
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2019 ◽
Vol 09
(04)
◽
pp. 2150003