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

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

2011-10-19

arxiv.org/abs/1110.4323v2

Mathematics

Probability

16 pages; reorganized and removed assumption (iv); added results concerning off-diagonal entries

Scientific paper

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.

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