article published yes László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 Horng Yau author LaEr department We consider generalized Wigner ensembles and general β-ensembles with analytic potentials for any β ≥ 1. The recent universality results in particular assert that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum are universal in the sense that they coincide with those of the corresponding Gaussian β-ensembles. In this article, we show that local averaging is not necessary for this result, i.e. we prove that the single gap distributions in the bulk are universal. In fact, with an additional step, our result can be extended to any C4(ℝ) potential. European Mathematical Society2015 eng 1211.3786 00036082290000310.4171/JEMS/548 1781927 - 2036 Erdös, L., &#38; Yau, H. (2015). Gap universality of generalized Wigner and β ensembles. <i>Journal of the European Mathematical Society</i>. European Mathematical Society. <a href="https://doi.org/10.4171/JEMS/548">https://doi.org/10.4171/JEMS/548</a> Erdös, László, and Horng Yau. “Gap Universality of Generalized Wigner and β Ensembles.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society, 2015. <a href="https://doi.org/10.4171/JEMS/548">https://doi.org/10.4171/JEMS/548</a>. L. Erdös, H. Yau, Journal of the European Mathematical Society 17 (2015) 1927–2036. Erdös L, Yau H. 2015. Gap universality of generalized Wigner and β ensembles. Journal of the European Mathematical Society. 17(8), 1927–2036. L. Erdös and H. Yau, “Gap universality of generalized Wigner and β ensembles,” <i>Journal of the European Mathematical Society</i>, vol. 17, no. 8. European Mathematical Society, pp. 1927–2036, 2015. Erdös, László, and Horng Yau. “Gap Universality of Generalized Wigner and β Ensembles.” <i>Journal of the European Mathematical Society</i>, vol. 17, no. 8, European Mathematical Society, 2015, pp. 1927–2036, doi:<a href="https://doi.org/10.4171/JEMS/548">10.4171/JEMS/548</a>. Erdös L, Yau H. Gap universality of generalized Wigner and β ensembles. <i>Journal of the European Mathematical Society</i>. 2015;17(8):1927-2036. doi:<a href="https://doi.org/10.4171/JEMS/548">10.4171/JEMS/548</a> 15082018-12-11T11:52:26Z2025-09-23T09:08:38Z