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- W4287164046 abstract "We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter $z$ as the dimension tends to infinity. For $z$ away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in [arXiv:1908.01653]. On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter $z$ becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula [arXiv:0707.2929] in a regime where the main contribution comes from a three dimensional saddle manifold." @default.
- W4287164046 created "2022-07-25" @default.
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- W4287164046 date "2021-05-28" @default.
- W4287164046 modified "2023-10-18" @default.
- W4287164046 title "Density of small singular values of the shifted real Ginibre ensemble" @default.
- W4287164046 doi "https://doi.org/10.48550/arxiv.2105.13720" @default.
- W4287164046 hasPublicationYear "2021" @default.
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