On an average over the Gaussian Unitary Ensemble
Mathematical Physics
2010-04-13 v1 math.MP
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.
Keywords
Cite
@article{arxiv.0903.5450,
title = {On an average over the Gaussian Unitary Ensemble},
author = {F. Mezzadri and M. Y. Mo},
journal= {arXiv preprint arXiv:0903.5450},
year = {2010}
}
Comments
28 pages, 3 figures