Singularity dominated strong fluctuations for some random matrix averages

PJ Forrester, JP Keating

Research output: Contribution to journalArticle (Academic Journal)

15 Citations (Scopus)

Abstract

The circular and Jacobi ensembles of random matrices have their eigenvalue support on the unit circle of the complex plane and the interval (0,1) of the real line respectively. The averaged value of the modulus of the corresponding characteristic polynomial raised to the power 2mu diverges, for 2muless than or equal to-1, at points approaching the eigenvalue support. Using the theory of generalized hypergeometric functions based on Jack polynomials, the functional form of the leading asymptotic behaviour is established rigorously. In the circular ensemble case this confirms a conjecture of Berry and Keating.
Translated title of the contributionSingularity dominated strong fluctuations for some random matrix averages
Original languageEnglish
Pages (from-to)119 - 131
Number of pages13
JournalCommunications in Mathematical Physics
Volume250 (1)
DOIs
Publication statusPublished - Aug 2004

Bibliographical note

Publisher: Springer
Other identifier: IDS Number: 863KF

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