article published yes Paul Bourgade author László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 Horngtzer Yau author LaEr department Glutamaterge synaptische Übertragung und Plastizität in hippocampalen Mikroschaltkreisen project We prove the edge universality of the beta ensembles for any β ≥ 1, provided that the limiting spectrum is supported on a single interval, and the external potential is C4 and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class C4. Springer2014 eng 1306.5728 00034149170000710.1007/s00220-014-2120-z 3321261 - 353 Bourgade P, Erdös L, Yau H. 2014. Edge universality of beta ensembles. Communications in Mathematical Physics. 332(1), 261–353. Bourgade, Paul, et al. “Edge Universality of Beta Ensembles.” <i>Communications in Mathematical Physics</i>, vol. 332, no. 1, Springer, 2014, pp. 261–353, doi:<a href="https://doi.org/10.1007/s00220-014-2120-z">10.1007/s00220-014-2120-z</a>. Bourgade, Paul, László Erdös, and Horngtzer Yau. “Edge Universality of Beta Ensembles.” <i>Communications in Mathematical Physics</i>. Springer, 2014. <a href="https://doi.org/10.1007/s00220-014-2120-z">https://doi.org/10.1007/s00220-014-2120-z</a>. P. Bourgade, L. Erdös, H. Yau, Communications in Mathematical Physics 332 (2014) 261–353. Bourgade, P., Erdös, L., &#38; Yau, H. (2014). Edge universality of beta ensembles. <i>Communications in Mathematical Physics</i>. Springer. <a href="https://doi.org/10.1007/s00220-014-2120-z">https://doi.org/10.1007/s00220-014-2120-z</a> Bourgade P, Erdös L, Yau H. Edge universality of beta ensembles. <i>Communications in Mathematical Physics</i>. 2014;332(1):261-353. doi:<a href="https://doi.org/10.1007/s00220-014-2120-z">10.1007/s00220-014-2120-z</a> P. Bourgade, L. Erdös, and H. Yau, “Edge universality of beta ensembles,” <i>Communications in Mathematical Physics</i>, vol. 332, no. 1. Springer, pp. 261–353, 2014. 19372018-12-11T11:54:48Z2025-09-29T12:08:21Z