@article{15063,
  abstract     = {We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395).},
  author       = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
  issn         = {2690-1005},
  journal      = {Probability and Mathematical Physics},
  keywords     = {General Medicine},
  number       = {1},
  pages        = {101--146},
  publisher    = {Mathematical Sciences Publishers},
  title        = {{Optimal lower bound on the least singular value of the shifted Ginibre ensemble}},
  doi          = {10.2140/pmp.2020.1.101},
  volume       = {1},
  year         = {2020},
}