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.
The paper is concerned with the correlation functions of the characteristic polynomials of real random matrices with independent entries. The asymptotic behavior of the correlation functions is established in the form of a certain integral over unitary self-dual matrices with respect to the invariant measure. The integral is computed in the case of the second order correlation function. From the obtained asymptotics it is clear that the correlation functions behave like that for the Real Ginibre Ensemble up to a factor depending only on the fourth absolute moment of the common probability law of the matrix entries.
We consider asymptotics of the correlation functions of characteristic polynomials corresponding to random weighted G(n, p n ) Erdős-Rényi graphs with Gaussian weights in the case of finite p and also when p → ∞. It is shown that for finite p the second correlation function demonstrates a kind of transition: when p < 2 it factorizes in the limit n → ∞, while for p > 2 there appears an interval (−λ * ( p), λ * ( p)) such that for λ 0 ∈ (−λ * ( p), λ * ( p)) the second correlation function behaves like that for Gaussian unitary ensemble (GUE), while for λ 0 outside the interval the second correlation function is still factorized. For p → ∞ there is also a threshold in the behavior of the second correlation function near λ 0 = ±2: for p n 2/3 the second correlation function factorizes, whereas for p n 2/3 it behaves like that for GUE. For any rate of p → ∞ the asymptotics of correlation functions of any even order for λ 0 ∈ (−2, 2) coincide with that for GUE.
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