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On the second-order correlation function of the characteristic polynomial of a real symmetric Wigner matrix. (English) Zbl 1189.60019

Summary: We consider the asymptotic behaviour of the second-order correlation function of the characteristic polynomial of a real symmetric random matrix. Our main result is that the existing result for a random matrix from the Gaussian Orthogonal Ensemble, obtained by E. Brézin and S. Hikami [Commun. Math. Phys. 223, No. 2, 363–382 (2001; Zbl 0987.15012)], essentially continues to hold for a general real symmetric Wigner matrix. To obtain this result, we adapt the approach by F. Götze and H. Kösters [Commun. Math. Phys. 285, No. 3, 1183–1205 (2009; Zbl 1193.15035)], who proved the analogous result for the Hermitian case.

MSC:

60B20 Random matrices (probabilistic aspects)
15B52 Random matrices (algebraic aspects)
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