@article{17375,
  abstract     = {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.},
  author       = {Cipolloni, Giorgio and Erdös, László and Xu, Yuanyuan},
  issn         = {0022-2488},
  journal      = {Journal of Mathematical Physics},
  number       = {6},
  publisher    = {AIP Publishing},
  title        = {{Precise asymptotics for the spectral radius of a large random matrix}},
  doi          = {10.1063/5.0209705},
  volume       = {65},
  year         = {2024},
}