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Spectral correlations: Understanding oscillatory contributions

Mehlig, B. and Wilkinson, M. (2001) Spectral correlations: Understanding oscillatory contributions. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 63 (4). 045203-1. ISSN 1063-651X

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We give a different derivation of a relation obtained using a supersymmetric nonlinear sigma model by Andreev and Altshuler [Phys. Rev. Lett. 72, 902 (1995)], which connects smooth and oscillatory components of spectral correlation functions. We show that their result is not specific to the random matrix theory. Also, we show that despite an apparent contradiction, the results obtained using their formula are consistent with earlier perspectives on random matrix models.