On an Average over the Gaussian Unitary Ensemble
Copyright policy )On an Average over the Gaussian Unitary Ensemble
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.
28 pages, 3 figures
- University of Bristol United Kingdom
35Q15 (Secondary), FOS: Physical sciences, Mathematical Physics (math-ph), 15A52 (Primary); 35Q15 (Secondary), 530, Mathematical Physics, 510, 15A52 (Primary)
35Q15 (Secondary), FOS: Physical sciences, Mathematical Physics (math-ph), 15A52 (Primary); 35Q15 (Secondary), 530, Mathematical Physics, 510, 15A52 (Primary)
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