The second correlation function of characteristic polynomials for non-Hermitian random band matrices is studied asymptotically in the critical regime W proportional to sqrt(N) as N and W tend to infinity.
Bulk universality for complex non-hermitian matrices with inde- pendent and identically distributed entries,arXiv:2310.11429v4(2023) 22
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Brown measure of a + c has real analytic density with classified edge singularities and internal zeros under regularity conditions on a and covariance of c, arising as ESD of diagonally deformed random matrices.
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Characteristic polynomials of non-Hermitian random band matrices near the threshold
The second correlation function of characteristic polynomials for non-Hermitian random band matrices is studied asymptotically in the critical regime W proportional to sqrt(N) as N and W tend to infinity.
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Brown measures of deformed $L^\infty$-valued circular elements
Brown measure of a + c has real analytic density with classified edge singularities and internal zeros under regularity conditions on a and covariance of c, arising as ESD of diagonally deformed random matrices.