Abstract
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 [2]. 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 |
|---|---|
| Original language | English |
| Pages (from-to) | 3486 - 3515 |
| Number of pages | 30 |
| Journal | International Mathematics Research Notices |
| Volume | 2009 |
| Issue number | 18 |
| DOIs | |
| Publication status | Published - 24 May 2009 |