The largest eigenvalue of small rank perturbations of Hermitian random matrices
By S. P'ech'e. 2004
249 citations recorded by the source corpus.
We compute the limiting eigenvalue statistics at the edge of the spectrum of large Hermitian random matrices perturbed by the addition of small rank deterministic matrices. We consider random Hermitian matrices with independent Gaussian entries Mij,i≤j with various expectations. We prove that the largest eigenvalue of such random matrices exhibits, in the large N limit, various limiting distributions depending on both the eigenvalues of the matrix and its rank. This rank is also allowed to increase with N in some restricted way.
Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/7c7f501ab01e4b9457cdead6af65ae5edf75c7e4
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In Discrete Mathematics and Combinatorics
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- On finite rank deformations of Wigner matrices (2011, unknown): “entries, in particular [30], [19], [26], [12], [13], [14], [8], [9], [10], [35].”
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- Limits of spiked random matrices I (2010, methodology): “Remark 1.6 The remarks following the previous theorem apply also to this theorem; the universality issue is discussed in Féral and Péché [25].”
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- Free Convolution with a Semicircular Distribution and Eigenvalues of Spiked Deformations of Wigner Matrices (2010, background): “In [30], S.”
- Fundamental limits of detection in the spiked Wigner model (2018, background): “Above this value, the first eigenvalue of the matrix Y detaches from the bulk (Capitaine, Donati-Martin and Féral (2009), Féral and Péché (2007), Péché (2006)).”
- Singular vector and singular subspace distribution for the matrix denoising model (2018, background): “The fluctuation of the extreme eigenvalues of various models have been considered in [2, 3, 7, 8, 9, 23, 24, 28, 14, 15, 42, 55, 34, 56, 59, 44].”
- Outliers in the spectrum of large deformed unitarily invariant models (2012, methodology): “See also [29, 4, 5] for sample covariance matrices, [24, 32, 22, 19, 33] for deformed Wigner models and [31] for information-plus-noise models.”