Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices
نویسندگان
چکیده
We consider N by deformed Wigner random matrices of the form XN=HN+AN, where HN is a real symmetric or complex Hermitian matrix and AN deterministic bounded diagonal matrix. prove universal Central Limit Theorem for linear eigenvalue statistics XN all mesoscopic scales both in spectral bulk at regular edges global density vanishes as square root. The method relies on studying characteristic function (Landon Sosoe (2018)) using cumulant expansion method, along with local laws Green (Ann. Probab. 48 (2020) 963–1001; Theory Related Fields 169 (2017) 257–352; J. Math. Phys. 54 (2013) 103504) analytic subordination properties free additive convolution (Dallaporta Fevrier (2019); Random Matrices Appl. 9 2050011). also analogous results high-dimensional sample covariance matrices.
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ژورنال
عنوان ژورنال: Annales de l'I.H.P
سال: 2021
ISSN: ['0246-0203', '1778-7017']
DOI: https://doi.org/10.1214/20-aihp1086