On an average over the Gaussian Unitary Ensemble

F Mezzadri, MY Mo

Research output: Contribution to journalArticle (Academic Journal)peer-review

12 Citations (Scopus)

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 contributionOn an average over the Gaussian Unitary Ensemble
Original languageEnglish
Pages (from-to)3486 - 3515
Number of pages30
JournalInternational Mathematics Research Notices
Volume2009
Issue number18
DOIs
Publication statusPublished - 24 May 2009

Bibliographical note

Publisher: Oxford University Press

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