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 Yuanyuan Xu author 7902bdb1-a2a4-11eb-a164-c9216f71aea30000-0003-1559-1205 LaEr department Random matrices beyond Wigner-Dyson-Mehta project We consider the spectral radius of a large random matrix X with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of X in Cipolloni et al., Ann. Probab. 51(6), 2192–2242 (2023). To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of X − z for different complex shift parameters z using the Dyson Brownian Motion. AIP Publishing2024 eng 0022-2488 2210.15643 00125224070000210.1063/5.0209705 656 Cipolloni, G., Erdös, L., &#38; Xu, Y. (2024). Precise asymptotics for the spectral radius of a large random matrix. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href="https://doi.org/10.1063/5.0209705">https://doi.org/10.1063/5.0209705</a> Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2024. <a href="https://doi.org/10.1063/5.0209705">https://doi.org/10.1063/5.0209705</a>. Cipolloni, Giorgio, et al. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” <i>Journal of Mathematical Physics</i>, vol. 65, no. 6, 063302, AIP Publishing, 2024, doi:<a href="https://doi.org/10.1063/5.0209705">10.1063/5.0209705</a>. G. Cipolloni, L. Erdös, and Y. Xu, “Precise asymptotics for the spectral radius of a large random matrix,” <i>Journal of Mathematical Physics</i>, vol. 65, no. 6. AIP Publishing, 2024. Cipolloni G, Erdös L, Xu Y. 2024. Precise asymptotics for the spectral radius of a large random matrix. Journal of Mathematical Physics. 65(6), 063302. Cipolloni G, Erdös L, Xu Y. Precise asymptotics for the spectral radius of a large random matrix. <i>Journal of Mathematical Physics</i>. 2024;65(6). doi:<a href="https://doi.org/10.1063/5.0209705">10.1063/5.0209705</a> G. Cipolloni, L. Erdös, Y. Xu, Journal of Mathematical Physics 65 (2024). 173752024-08-04T22:01:22Z2025-09-08T08:44:57Z