We prove that the asymptotic behavior of the second mixed moment of the characteristic polynomials of the N × N 1D Gaussian real symmetric band matrices with the width of the band W ≫ N1/2 coincides with those for the Gaussian orthogonal ensemble. Here, we adapt the approach of Shcherbina [Commun. Math. Phys. 328, 45-82 (2014)], where the Hermitian case was considered.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics