Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture

Diaconis, Persi

doi:10.1090/S0273-0979-03-00975-3

Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture
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Bull. Amer. Math. Soc. 40 (2003), 155-178 Request permission

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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