On the rightmost eigenvalue of non-Hermitian random matrices

Summary

We obtain a precise three-term expansion for the right-most eigenvalue of IID random matrices, precisely matching the corresponding result for Ginibre matrices which may be obtained with more algebraic methods.

Abstract

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.

Paper

2206.04448.pdf