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On the Averages of Characteristic Polynomials From Classical Groups |
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| Authors: | Daniel Bump Alex Gamburd |
| Institution: | (1) Department of Mathematics, Stanford University, Stanford, CA 94305, USA;(2) Department of Mathematics, University of California, Santa Cruz, CA 95064, USA;(3) Present address: School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA |
| Abstract: | We provide an elementary and self-contained derivation of formulae for averages of products and ratios of characteristic polynomials of random matrices from classical groups using classical results due to Weyl and Littlewood. The first author was supported in part by the NSF grant FRG DMS-0354662. The second author was supported in part by the NSF postdoctoral fellowship and by the NSF grant DMS-0501245. |
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