We study the asymptotic limit for large matrix dimension N of the partition function of the unitary ensemble (β = 2) with weight . We compute the leading-order term of the partition function and the coefficients of its Taylor expansion. Our results are valid in the region . Such a partition function contains all the information on a new statistics of the eigenvalues of matrices in the Gaussian unitary ensemble that was introduced by Berry and Shukla . It can also be interpreted as the moment-generating function of the singular linear statistics .
|Translated title of the contribution||On an average over the Gaussian Unitary Ensemble|
|Pages (from-to)||3486 - 3515|
|Number of pages||30|
|Journal||International Mathematics Research Notices|
|Publication status||Published - 24 May 2009|