Langevin dynamics on spiked Wigner matrices achieve O(log N) mixing from symmetric initializations even below the critical temperature, while worst-case mixing times are exponential with rate equal to the free-energy difference between spiked and null models.
Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices.Ann
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Finite-rank normal perturbations of large rotationally invariant non-Hermitian random matrices produce outlier eigenvalues whose positions and fluctuations, together with the associated eigenvectors, are characterized in a unified framework that includes the Hermitian case.
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Mixing times of Langevin dynamics for spiked matrix models
Langevin dynamics on spiked Wigner matrices achieve O(log N) mixing from symmetric initializations even below the critical temperature, while worst-case mixing times are exponential with rate equal to the free-energy difference between spiked and null models.
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The eigenvalues and eigenvectors of finite-rank normal perturbations of large rotationally invariant non-Hermitian matrices
Finite-rank normal perturbations of large rotationally invariant non-Hermitian random matrices produce outlier eigenvalues whose positions and fluctuations, together with the associated eigenvectors, are characterized in a unified framework that includes the Hermitian case.