On the Correlation Functions of the Characteristic Polynomials of Non-Hermitian Random Matrices with Independent Entries

Abstract

The paper is concerned with the asymptotic behavior of the correlation functions of the characteristic polynomials of non-Hermitian random matrices with independent entries. It is shown that the correlation functions behave like that for the Complex Ginibre Ensemble up to a factor depending only on the fourth absolute moment of the common probability law of the matrix entries.

22 pages, 1 table; the proof is generalized for the case of arbitrary $m$; a certain particular case is added to Theorem 1, some remarks added, notation changed, typos corrected, references added

References in corpus (2)

• On the moments of the characteristic polynomial of a Ginibre random matrix
• Universality for 1d random band matrices: sigma-model approximation

Cited by in corpus (4)

• Characteristic polynomials of complex random matrices and Painlevé transcendents
• Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble
• Complex symmetric, self-dual, and Ginibre random matrices: Analytical results for three classes of bulk and edge statistics
• Characteristic polynomials of products of Wigner matrices: finite-N results and Lyapunov universality