Dyson's constant in the asymptotics of the Fredholm determinant of the sine kernel

Details Dyson's constant in the asymptotics of the Fredholm determinant of the sine kernel Dyson's constant in the asymptotics of the Fredholm determinant of the sine kernel

2004-01-16

arxiv.org/abs/math/0401205v2

Mathematics

Functional Analysis

30 pages; v2: change of title, Thm.5.7 corrected, minor changes

Scientific paper

We prove that the asymptotics of the Fredholm determinant of $I-K_\alpha$, where $K_\alpha$ is the integral operator with the sine kernel $\sin(x-y)/(x-y)/\pi$ on the interval $[0,\alpha]$ is given by a formula which was conjectured by F.J. Dyson. The first and second order asymptotics as well as the higher order asymptotics except for the constant term have already been proved. In this paper we thus determine the constant term.

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