@article{12232,
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 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.},
author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
issn = {1424-0661},
journal = {Annales Henri Poincaré},
keywords = {Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics},
number = {11},
pages = {3981--4002},
publisher = {Springer Nature},
title = {{Density of small singular values of the shifted real Ginibre ensemble}},
doi = {10.1007/s00023-022-01188-8},
volume = {23},
year = {2022},
}