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Medientyp:
E-Artikel
Titel:
Density of small singular values of the shifted real Ginibre ensemble
Beteiligte:
Cipolloni, Giorgio
[VerfasserIn];
Erdös, László
[VerfasserIn];
Schröder, Dominik J
[VerfasserIn]
Erschienen:
Springer Nature, 2022
Erschienen in:Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré . 2022;23(11):3981-4002. doi: 10.1007/s00023-022-01188-8
Anmerkungen:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Beschreibung:
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 Cipolloni et al. (Prob Math Phys 1:101–146, 2020). 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 (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold.