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arXiv · 0903.5450

On an average over the Gaussian Unitary Ensemble

F. Mezzadri·M. Y. Mo
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Abstract

We study the asymptotic limit for large matrix dimension N of the partition function of the unitary ensemble with weight exp(-z^2/2x^2 + t/x - x^2/2). We compute the leading order term of the partition function and of the coefficients of its Taylor expansion. Our results are valid in the range N^(-1/2) < z < N^(1/4). Such partition function contains all the information on a new statistics of the eigenvalues of matrices in the Gaussian Unitary Ensemble (GUE) that was introduced by Berry and Shukla (J. Phys. A: Math. Theor., Vol. 41 (2008), 385202, arXiv:0807.3474). It can also be interpreted as the moment generating function of a singular linear statistics.

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F. Mezzadri, M. Y. Mo. 2009-03-31. On an average over the Gaussian Unitary Ensemble. https://doi.org/10.1093/imrn%2Frnp062

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