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Dyson’s constants in the asymptotics of the determinants of Wiener-Hopf-Hankel operators with the sine kernel. (English summary) Comm. Math. Phys. 272 (2007), no. 3, 683–698. For the integral operators K ± α on L 2 [0, α] with the Wiener-Hopf-Hankel sine kernels k ± (x, y) = sin(x − y) π(x − y) the author presents a proof of Dyson asymptotic formulas log det(I − K ± α) = sin(x + y) π(x + y), − α2 α log α log 2 log 2 3 4 2 8 24 4 2 ζ ′ (−1) + o(1), α → ∞ (where ζ denotes the Riemann zeta function). The main idea of the proof is based on the application of Fisher-Hartwig type formulas to certain determinants which are related to the Fredholm determinants det(I − K ± α). Reviewed by Luís P. Castr

Topics:
1. Barnes, E.B, The theory of the G-function. Quart. J. Pure Appl. Math. XXXI, 264–313 (1900

Year: 2010

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