Density of Small Singular Values of the Shifted Real Ginibre Ensemble

@article{Cipolloni2022DensityOS,
  title={Density of Small Singular Values of the Shifted Real Ginibre Ensemble},
  author={Giorgio Cipolloni and L{\'a}szl{\'o} Erdős and Dominik Schr{\"o}der},
  journal={Annales Henri Poincar{\'e}},
  year={2022}
}
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… 
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