Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/173676
Title: Tracy-widom law for the extreme eigenvalues of large signal-plus-noise matrices
Authors: Zhang, Zhixiang
Liu, Yiming
Pan, Guangming
Keywords: Physics
Issue Date: 2024
Source: Zhang, Z., Liu, Y. & Pan, G. (2024). Tracy-widom law for the extreme eigenvalues of large signal-plus-noise matrices. Bernoulli, 30(1), 448-474. https://dx.doi.org/10.3150/23-BEJ1604
Journal: Bernoulli
Abstract: Let S = R + X be an M × N matrix where R is the signal matrix and X is the noise matrix consisting of i.i.d. standardized entries. The signal matrix R is allowed to be full rank, which is rarely studied in literature compared with the low rank cases. Under a regularity condition of R that assures the square root behaviour of the spectral density near the edge, we prove that the largest eigenvalue of SS* has the Tracy-Widom distribution under a tail condition on the entries of X. Moreover, such a condition is proved to be necessary and sufficient to assure the Tracy-Widom law.
URI: https://hdl.handle.net/10356/173676
ISSN: 1350-7265
DOI: 10.3150/23-BEJ1604
Schools: School of Physical and Mathematical Sciences 
Rights: © 2024 Bernoulli Society for Mathematical Statistics and Probability. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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