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We prove that the asymptotic behavior of the second mixed moment of thecharacteristic polynomials of the 1D Gaussian real symmetric band matricescoincides with those for the Gaussian Orthogonal Ensemble (GOE). Here we adaptthe approach of T. Shcherbina'14, where the case of 1D Hermitian random bandmatrices was considered.

Universality of the second mixed moment of the characteristic polynomials of the 1D band matrices: real symmetric case