# Dyson's Constant in the Asymptotics of the Fredholm Determinant of the Sine Kernel

@article{Ehrhardt2004DysonsCI, title={Dyson's Constant in the Asymptotics of the Fredholm Determinant of the Sine Kernel}, author={Torsten Ehrhardt}, journal={Communications in Mathematical Physics}, year={2004}, volume={262}, pages={317-341} }

AbstractWe prove that the asymptotics of the Fredholm determinant of I−Kα, where Kα is the integral operator with the sine kernel on the interval [0, α], are given by
This formula was conjectured by Dyson. The proof for the first and second order asymptotics was given by Widom, and higher order asymptotics have also been determined. In this paper we identify the constant (or third order) term, which has been an outstanding problem for a long time.

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