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 contribution||Singularity dominated strong fluctuations for some random matrix averages|
|Pages (from-to)||119 - 131|
|Number of pages||13|
|Journal||Communications in Mathematical Physics|
|Publication status||Published - Aug 2004|
Bibliographical notePublisher: Springer
Other identifier: IDS Number: 863KF