Precise asymptotics for the spectral radius of a large random matrix Cipolloni, Giorgio ; https://orcid.org/0000-0002-4901-7992 Erdös, László ; https://orcid.org/0000-0001-5366-9603 Xu, Yuanyuan ; https://orcid.org/0000-0003-1559-1205 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 Publishing 2024 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/17375 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1063/5.0209705 info:eu-repo/semantics/altIdentifier/issn/0022-2488 info:eu-repo/semantics/altIdentifier/wos/001252240700002 info:eu-repo/semantics/altIdentifier/arxiv/2210.15643 info:eu-repo/semantics/openAccess