Abstract
We prove that the asymptotics of the Fredholm determinant of I−K α, where K α 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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