Recognizing linear structure in noisy matrices (Q556892)
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scientific article; zbMATH DE number 2182001
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Recognizing linear structure in noisy matrices |
scientific article; zbMATH DE number 2182001 |
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Recognizing linear structure in noisy matrices (English)
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23 June 2005
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A Wigner-noise is a random \(n\times n\) matrix that is symmetric, with the entries being independent mean zero, with uniformly bounded variance, and such that they are either uniformly bounded or Gaussian. The author [Linear Algebra Appl. 377, 219-240 (2004; Zbl 1042.15014)] studied the asymptotic behaviour of the eigenvalues of a symmetric block matrix perturbed by a Wigner-noise. In the paper under review, he extends the analysis to the case of blow-up matrices. Similar estimates are obtained for the perturbed eigenvalues, and for noisy weighted graphs. Cases where the blow-up matrix can be recognized from the perturbed matrix are analyzed.
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Wigner noise
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blow-up matrices
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perturbations of eigenvalues
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large deviations
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random matrix
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0.8521666
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0.84218717
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0.84094083
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0.8366328
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