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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture


Author: Persi Diaconis
Journal: Bull. Amer. Math. Soc. 40 (2003), 155-178
MSC (2000): Primary 00-02, 60B15
Published electronically: February 12, 2003
MathSciNet review: 1962294
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Abstract: Typical large unitary matrices show remarkable patterns in their eigenvalue distribution. These same patterns appear in telephone encryption, the zeros of Riemann's zeta function, a variety of physics problems, and in the study of Toeplitz operators. This paper surveys these applications and what is currently known about the patterns.


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Additional Information

Persi Diaconis
Affiliation: Department of Mathematics and Statistics, Stanford University, Stanford, CA 94305
Email: diaconis@math.stanford.edu

DOI: http://dx.doi.org/10.1090/S0273-0979-03-00975-3
PII: S 0273-0979(03)00975-3
Received by editor(s): October 10, 2002
Published electronically: February 12, 2003
Article copyright: © Copyright 2003 American Mathematical Society