Averages of ratios of characteristic polynomials for the compact classical groups are evaluated in terms of determinants whose dimensions are independent of the matrix rank. These formulas are shown to be equivalent to expressions for the same averages obtained in a previous study, which was motivated by applications to analytic number theory. Our approach uses classical methods of random matrix theory, in particular determinants and orthogonal polynomials, and can be considered more elementary than the method of Howe pairs used in the previous study.
|Translated title of the contribution||Averages of ratios of characteristic polynomials for the compact classical groups|
|Pages (from-to)||397 - 431|
|Number of pages||35|
|Journal||International Mathematics Research Notices|
|Publication status||Published - Feb 2005|
Bibliographical notePublisher: Hindawi Publishing Corporation
Other identifier: IDS Number: 915MS