On the rightmost eigenvalue of non-Hermitian random matrices

Giorgio Cipolloni, László Erdős, Yuanyuan Xu, Dominik Schröder

Published 2022-06-09Version 1

We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an $n\times n$ random matrix with independent identically distributed complex entries as $n$ tends to infinity. All terms in the expansion are universal.