Fluctuations of Matrix Entries of Analytic Functions of Non-Hermitian Random Matrices

Abstract: Consider an $n \times n$ non-Hermitian random matrix $M_n$ whose entries are independent real random variables. Under suitable conditions on the entries, we study the fluctuations of the entries of $f(M_n)$ as $n$ tends to infinity, where $f$ is analytic on an appropriate domain. This extends the results for symmetric random matrices to the non-Hermitian case.