On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix

Götze F, Kösters H (2009)
COMMUNICATIONS IN MATHEMATICAL PHYSICS 285(3): 1183-1205.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
We consider the asymptotics of the second-order correlation function of the characteristic polynomial of a random matrix. We show that the known result for a random matrix from the Gaussian Unitary Ensemble essentially continues to hold for a general Hermitian Wigner matrix. Our proofs rely on an explicit formula for the exponential generating function of the second-order correlation function of the characteristic polynomial. Furthermore, we show that the second-order correlation function of the characteristic polynomial is closely related to that of the permanental polynomial.
Erscheinungsjahr
Zeitschriftentitel
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Band
285
Ausgabe
3
Seite(n)
1183-1205
ISSN
PUB-ID

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Götze F, Kösters H. On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2009;285(3):1183-1205.
Götze, F., & Kösters, H. (2009). On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 285(3), 1183-1205. doi:10.1007/s00220-008-0544-z
Götze, F., and Kösters, H. (2009). On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix. COMMUNICATIONS IN MATHEMATICAL PHYSICS 285, 1183-1205.
Götze, F., & Kösters, H., 2009. On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 285(3), p 1183-1205.
F. Götze and H. Kösters, “On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix”, COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 285, 2009, pp. 1183-1205.
Götze, F., Kösters, H.: On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 285, 1183-1205 (2009).
Götze, Friedrich, and Kösters, Holger. “On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix”. COMMUNICATIONS IN MATHEMATICAL PHYSICS 285.3 (2009): 1183-1205.