On the Second-Order Correlation Function of the Characteristic Polynomial of a Real Symmetric Wigner Matrix
Holger Kösters, University of Bielefeld
Abstract
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 Brézin and Hikami (2001),
essentially continues to hold
for a general real symmetric Wigner matrix.
To obtain this result, we adapt the approach
by Götze and Kösters (2008),
who proved the analogous result
for the Hermitian case.
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