On finite rank deformations of Wigner matrices
By A. Pizzo, David Renfrew, Alexander Soshnikov. 2011
110 citations recorded by the source corpus.
We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrices under the assumption that the absolute values of the off-diagonal matrix entries have uniformly bounded fifth moment and the abso- lute values of the diagonal entries have uniformly bounded third moment. Using our recent results on the fluctuation of resolvent entries (On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries, Unpub- lished manuscript; Fluctuations of matrix entries of regular functions of Wigner matrices, Unpublished manuscript) and ideas from (Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices, Unpublished manuscript), we extend the results by Capitaine, Donati-Martin, and Feral (Ann. Probab. 37 (2009) 1–47; Ann. Inst. Henri Poincare Probab. Stat. 48 (2012) 107–133).
Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/f13f523700d46090135c3a53841f467b50970b67
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Citations in the corpus
- 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.”
- 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].”
- Random matrix theory in statistics: A review (2014, background): “…deformed Wigner ensembles with the associated phase transition behavior exhibited by the extreme eigenvalues (see Benaych-Georges et al., 2011; Capitaine et al., 2009; Féral and Péché, 2007; Pizzo et al., 2013; Renfrew and Soshnikov, 2013; Knowles and Yin, 2011, 2012 and the references therein).”
- Outlier Eigenvalues for Deformed I.I.D. Random Matrices (2014, unknown): “Note that motivated by the seminal article of Baik, Ben Arous and Péché [6], previous works are devoted to the study of the outlier eigenvalues of deformed random Hermitian matrix models, see notably [4, 7, 8, 9, 10, 19, 21, 22, 23, 28, 34, 35, 36, 37, 41, 43, 45, 46].”
- The Isotropic Semicircle Law and Deformation of Wigner Matrices (2011, methodology): “Section 6 is devoted to the proof of deviation estimates for the eigenvalues of HCA.”
- Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails (2015, methodology): “10, we prove an isotropic property of the semi-circular law using the estimates in [23] of the entries of the resolvent of Wigner matrices.”
- On the principal components of sample covariance matrices (2014, background): “Finally, a related class of models, so-called deformed Wigner matrices, have been the subject of much attention in recent years; we refer to [27,29,37,38] for more details; in particular, the joint distribution of all outliers was derived in [27].”
- Statistical inference for principal components of spiked covariance matrices (2020, methodology): “[73] A.”