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We study the fundamental limits of detecting the presence of an additive rank-one perturbation, or spike, to a Wigner matrix.
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Some rigorous results on the Sherrington–Kirkpatrick spin glass model
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Spin Glass Theory and Beyond
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Recipes for metastable states in spin glasses
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Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
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Eigenvalues of large sample covariance matrices of spiked population models
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The largest eigenvalue of small rank perturbations of Hermitian random matrices
Péché, S. (2006) · 2006
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The largest eigenvalue of rank one deformation of large Wigner matrices
Féral, D. and Péché, S. (2007) · 2007
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Central limit theorems for eigenvalues in a spiked population model
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Amini, A. A. and Wainwright, M. J. (2009) · 2009
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Testing in high-dimensional spiked models
Johnstone, I. M. and Onatski, A. (2015) · 2015
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Phase transitions in sparse PCA
Lesieur, T., Krzakala, F., and Zdeborová, L. (2015) · 2015
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Fluctuations of the free energy of the spherical Sherrington–Kirkpatrick model
Baik, J. and Lee, J. O. (2016) · 2016
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Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
Barbier, J., Dia, M., Macris, N., Krzakala, F., Lesieur, T., and Zdeborová, L. (2016) · 2016
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Asymptotic mutual information for the binary stochastic block model
Deshpande, Y., Abbé, E., and Montanari, A. (2016) · 2016
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Mutual information in rank-one matrix estimation
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Fundamental limits of symmetric low-rank matrix estimation
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On the optimality and sub-optimality of PCA for spiked random matrix models
Perry, A., Wein, A. S., Bandeira, A. S., and Moitra, A. (2016) · 2016
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Banks, J., Moore, C., Vershynin, R., Verzelen, N., and Xu, J. (2017) · 2017
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Contiguity and non-reconstruction results for planted partition models: the dense case
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