Non–Hermitian spectral universality at critical points

article Non–Hermitian spectral universality at critical points epub_ahead yes Giorgio Cipolloni author 42198EFA-F248-11E8-B48F-1D18A9856A870000-0002-4901-7992 László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 Hong Chang Ji author LaEr department Random matrices beyond Wigner-Dyson-Mehta project For general large non–Hermitian random matrices X and deterministic normal deformations A, we prove that the local eigenvalue statistics of A + X close to the critical edge points of its spectrum are universal. This concludes the proof of the third and last remaining typical universality class for non–Hermitian random matrices (for normal deformations), after bulk and sharp edge universalities have been established in recent years. Springer Nature2025 eng Probability Theory and Related Fields 0178-8051 1432-2064 00149309190000110.1007/s00440-025-01384-7 Cipolloni, G., Erdös, L., & Ji, H. C. (2025). Non–Hermitian spectral universality at critical points. Probability Theory and Related Fields. Springer Nature. <a href="https://doi.org/10.1007/s00440-025-01384-7">https://doi.org/10.1007/s00440-025-01384-7</a> Cipolloni G, Erdös L, Ji HC. Non–Hermitian spectral universality at critical points. Probability Theory and Related Fields. 2025. doi:<a href="https://doi.org/10.1007/s00440-025-01384-7">10.1007/s00440-025-01384-7</a> Cipolloni, Giorgio, László Erdös, and Hong Chang Ji. “Non–Hermitian Spectral Universality at Critical Points.” Probability Theory and Related Fields. Springer Nature, 2025. <a href="https://doi.org/10.1007/s00440-025-01384-7">https://doi.org/10.1007/s00440-025-01384-7</a>. G. Cipolloni, L. Erdös, and H. C. Ji, “Non–Hermitian spectral universality at critical points,” Probability Theory and Related Fields. Springer Nature, 2025. Cipolloni G, Erdös L, Ji HC. 2025. Non–Hermitian spectral universality at critical points. Probability Theory and Related Fields., 050603. Cipolloni, Giorgio, et al. “Non–Hermitian Spectral Universality at Critical Points.” Probability Theory and Related Fields, 050603, Springer Nature, 2025, doi:<a href="https://doi.org/10.1007/s00440-025-01384-7">10.1007/s00440-025-01384-7</a>. G. Cipolloni, L. Erdös, H.C. Ji, Probability Theory and Related Fields (2025). 197372025-05-25T22:16:59Z2026-06-18T18:17:57Z