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Random matrices in nuclear physics and number theory. (English) Zbl 0594.60067
Random matrices and their applications, Proc. AMS-IMS-SIAM Joint Summer Res. Conf., Brunswick/Maine 1984, Contemp. Math. 50, 295-309 (1986).
[For the entire collection see Zbl 0581.00014.]
This is a very fascinating little paper in which the author describes the interrelationships between 1) the energy spectrum of total scattering cross-sections of neutrons, 2) the eigenvalues of random matrices, 3) the zeros of the Riemann zeta function.
Furthermore the author presents very interesting formulas for determining the joint probability distribution of the eigenvalues of random matrices. When deriving these formulas the author uses matrices with quaternions as elements.
Reviewer: T.Kaijser

MSC:
60H99 Stochastic analysis
15B52 Random matrices (algebraic aspects)
81U99 Quantum scattering theory
15B33 Matrices over special rings (quaternions, finite fields, etc.)
11M06 \(\zeta (s)\) and \(L(s, \chi)\)