For a spiked Wigner model with power-law inhomogeneous noise variances, the BBP transition is non-monotonic and inhomogeneous noise can enhance signal detectability.
The eigenvalues and eigenvectors of finite-rank normal perturbations of large rotationally invariant non-Hermitian matrices
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abstract
We study finite-rank normal deformations of rotationally invariant non-Hermitian random matrices. Extending the classical Baik-Ben Arous-P\'ech\'e (BBP) framework, we characterize the emergence and fluctuations of outlier eigenvalues in models of the form $\mathbf{A} + \mathbf{T}$, where $\mathbf{A}$ is a large rotationally invariant non-Hermitian random matrix and $\mathbf{T}$ is a finite-rank normal perturbation. We also describe the corresponding eigenvector behavior. Our results provide a unified framework encompassing both Hermitian and non-Hermitian settings, thereby generalizing several known cases.
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Local operators in quantum chaotic systems cascade toward non-local fractal structures whose dimension is tied by unitarity to the decay rate of local correlations, demonstrated exactly in dual-unitary circuits and numerically in others.
Spectral boundaries of A + B (A deterministic, B rotationally invariant random non-Hermitian) are given by simple equations depending on the R1 and R2 transforms of B in the large-N limit.
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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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Quantum many-body operator cascade as a route to chaos
Local operators in quantum chaotic systems cascade toward non-local fractal structures whose dimension is tied by unitarity to the decay rate of local correlations, demonstrated exactly in dual-unitary circuits and numerically in others.
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Spectral boundaries of deterministic matrices deformed by rotationally invariant random non-Hermitian ensembles
Spectral boundaries of A + B (A deterministic, B rotationally invariant random non-Hermitian) are given by simple equations depending on the R1 and R2 transforms of B in the large-N limit.