# Dyson’s Constants in the Asymptotics of the Determinants of Wiener-Hopf-Hankel Operators with the Sine Kernel

@article{Ehrhardt2007DysonsCI, title={Dyson’s Constants in the Asymptotics of the Determinants of Wiener-Hopf-Hankel Operators with the Sine Kernel}, author={T. Ehrhardt}, journal={Communications in Mathematical Physics}, year={2007}, volume={272}, pages={683-698} }

AbstractLet $$K_\alpha^\pm $$ stand for the integral operators with the sine kernels $$\frac{\sin(x-y)}{\pi(x-y)} \pm \frac{\sin(x+y)}{\pi(x+y)}$$ acting on L2[0,α]. Dyson conjectured that the asymptotics of the Fredholm determinants of $$I-K_\alpha^\pm$$ are given by
$$ \log\det(I-K_{\alpha}^\pm) = -\frac{\alpha^2}{4}\mp \frac{\alpha}{2}-\frac{\log\alpha}{8}+\frac{\log 2}{24}\pm \frac{\log 2}{4} +\frac{3}{2} \zeta'(-1)+o(1),$$as α→∞. In this paper we are going to give a proof of these two… CONTINUE READING

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