For a spiked Wigner model with power-law inhomogeneous noise variances, the BBP transition is non-monotonic and inhomogeneous noise can enhance signal detectability.
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For quadratic Euclidean random matrices, the average largest eigenvalue is explicitly determined by low-order moments of the point distribution, while the top eigenvector components concentrate on a hypersurface controlled by the same parameters.
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BBP transition and the leading eigenvector of the spiked Wigner model with inhomogeneous noise
For a spiked Wigner model with power-law inhomogeneous noise variances, the BBP transition is non-monotonic and inhomogeneous noise can enhance signal detectability.
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Largest eigenvalue and top eigenvector statistics of large Euclidean random matrices
For quadratic Euclidean random matrices, the average largest eigenvalue is explicitly determined by low-order moments of the point distribution, while the top eigenvector components concentrate on a hypersurface controlled by the same parameters.