article published yes Giorgio Cipolloni author 42198EFA-F248-11E8-B48F-1D18A9856A870000-0002-4901-7992 László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 Dominik J Schröder author 408ED176-F248-11E8-B48F-1D18A9856A870000-0002-2904-1856 LaEr department Following E. Wigner’s original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched versions of bulk universality that has so far only been proven in annealed sense with respect to the probability space of the matrix ensemble. https://research-explorer.ista.ac.at/download/11741/14054/2023_ProbabilityTheory_Cipolloni.pdf application/pdfno Springer Nature2023 eng 0178-8051 1432-2064 2106.10200 00083034450000110.1007/s00440-022-01156-7 1851183–1218 G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 185 (2023) 1183–1218. Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Quenched universality for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href="https://doi.org/10.1007/s00440-022-01156-7">https://doi.org/10.1007/s00440-022-01156-7</a> G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed Wigner matrices,” <i>Probability Theory and Related Fields</i>, vol. 185. Springer Nature, pp. 1183–1218, 2023. Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218. Cipolloni G, Erdös L, Schröder DJ. Quenched universality for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. 2023;185:1183–1218. doi:<a href="https://doi.org/10.1007/s00440-022-01156-7">10.1007/s00440-022-01156-7</a> Cipolloni, Giorgio, et al. “Quenched Universality for Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>, vol. 185, Springer Nature, 2023, pp. 1183–1218, doi:<a href="https://doi.org/10.1007/s00440-022-01156-7">10.1007/s00440-022-01156-7</a>. Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality for Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s00440-022-01156-7">https://doi.org/10.1007/s00440-022-01156-7</a>. 117412022-08-07T22:02:00Z2024-10-09T21:03:02Z