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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.18501 |
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| _version_ | 1866909919894044672 |
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| author | Forner, Niklas Maloney, Alexander Rosenow, Bernd |
| author_facet | Forner, Niklas Maloney, Alexander Rosenow, Bernd |
| contents | Random-matrix theory helps disentangle signal from noise in large data sets. We analyze rectangular $p \times q$ matrices $W = W_0 + M$ in which the noise $M$ generates a Marchenko-Pastur bulk, whereas the signal $W_0$ injects an extensive set of degenerate singular values. Keeping $\mathrm{rank}$ $W_0/q$ finite as $p,q \to \infty$, we show that the singular value density obeys a quartic equation and derive explicit asymptotics in the strong-signal regime. The resulting generalized Baik-Ben Arous-Péché phase diagram yields a scaling law for the critical signal strength and clarifies how a finite density of spikes reshapes the bulk edges. Numerical simulations validate the theory and illustrate its relevance for high-dimensional inference tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18501 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | BBP Phase Transition for an Extensive Number of Outliers Forner, Niklas Maloney, Alexander Rosenow, Bernd Disordered Systems and Neural Networks Random-matrix theory helps disentangle signal from noise in large data sets. We analyze rectangular $p \times q$ matrices $W = W_0 + M$ in which the noise $M$ generates a Marchenko-Pastur bulk, whereas the signal $W_0$ injects an extensive set of degenerate singular values. Keeping $\mathrm{rank}$ $W_0/q$ finite as $p,q \to \infty$, we show that the singular value density obeys a quartic equation and derive explicit asymptotics in the strong-signal regime. The resulting generalized Baik-Ben Arous-Péché phase diagram yields a scaling law for the critical signal strength and clarifies how a finite density of spikes reshapes the bulk edges. Numerical simulations validate the theory and illustrate its relevance for high-dimensional inference tasks. |
| title | BBP Phase Transition for an Extensive Number of Outliers |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2511.18501 |