Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
High powers of random elements of compact Lie groups
Download PDF
Download PDF
  • Published: 01 October 2002

High powers of random elements of compact Lie groups

  • E.M. Rains1 

Probability Theory and Related Fields volume 107, pages 219–241 (1997)Cite this article

  • 398 Accesses

  • 39 Citations

  • Metrics details

Summary.

If a random unitary matrix \(U\) is raised to a sufficiently high power, its eigenvalues are exactly distributed as independent, uniform phases. We prove this result, and apply it to give exact asymptotics of the variance of the number of eigenvalues of \(U\) falling in a given arc, as the dimension of \(U\) tends to infinity. The independence result, it turns out, extends to arbitrary representations of arbitrary compact Lie groups. We state and prove this more general theorem, paying special attention to the compact classical groups and to wreath products. This paper is excerpted from the author's doctoral thesis, [9].

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Harvard University, Cambridge, MA 02138, USA (e-mail: rains@ccr-p.ida.org), Cambridge, MA, USA

    E.M. Rains

Authors
  1. E.M. Rains
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 15 October 1995 / In revised form: 7 March 1996

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Rains, E. High powers of random elements of compact Lie groups. Probab Theory Relat Fields 107, 219–241 (1997). https://doi.org/10.1007/s004400050084

Download citation

  • Published: 01 October 2002

  • Issue Date: February 1997

  • DOI: https://doi.org/10.1007/s004400050084

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

  • Mathematics Subject Classification (1991):60B15, 22E99
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature