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Images of eigenvalue distributions under power maps
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  • Published: April 2003

Images of eigenvalue distributions under power maps

  • Eric M. Rains1 

Probability Theory and Related Fields volume 125, pages 522–538 (2003)Cite this article

Abstract.

 In [9], it was shown that if U is a random n×n unitary matrix, then for any p≥n, the eigenvalues of U p are i.i.d. uniform; similar results were also shown for general compact Lie groups. We study what happens when p<n instead. For the classical groups, we find that we can describe the eigenvalue distribution of U p in terms of the eigenvalue distributions of smaller classical groups; the earlier result is then a special case. The proofs rely on the fact that a certain subgroup of the Weyl group is itself a Weyl group. We generalize this fact, and use it to study the power-map problem for general compact Lie groups.

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Authors and Affiliations

  1. AT&T Labs-Research, Florham Park, NJ, USA and California Inst. of Technology, Department, Mathematics 253-37, Pasadena, CA 91125-0001, USA., , , , , , US

    Eric M. Rains

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  1. Eric M. Rains
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Additional information

Received: 19 December 2000 / Revised version: 7 August 2002 / Published online: 21 February 2003

Permanent address: Center for Communications Research, Princeton, NJ, USA. e-mail: rains@idaccr.org

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Rains, E. Images of eigenvalue distributions under power maps. Probab. Theory Relat. Fields 125, 522–538 (2003). https://doi.org/10.1007/s00440-002-0250-2

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  • Issue Date: April 2003

  • DOI: https://doi.org/10.1007/s00440-002-0250-2

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Keywords

  • Unitary Matrix
  • Early Result
  • Classical Group
  • Weyl Group
  • Eigenvalue Distribution
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