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On the Averages of Characteristic Polynomials From Classical Groups

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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.

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Author notes

  1. Alex Gamburd

    Present address: School of Mathematics, Institute for Advanced Study, Princeton, NJ, 08540, USA

Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Daniel Bump & Alex Gamburd

  2. Department of Mathematics, University of California, Santa Cruz, CA, 95064, USA

    Alex Gamburd

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  1. Daniel Bump
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  2. Alex Gamburd
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Correspondence to Alex Gamburd.

Additional information

Communicated by P. Sarnak

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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Bump, D., Gamburd, A. On the Averages of Characteristic Polynomials From Classical Groups. Commun. Math. Phys. 265, 227–274 (2006). https://doi.org/10.1007/s00220-006-1503-1

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