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

  title={Dyson's Constant in the Asymptotics of the Fredholm Determinant of the Sine Kernel},
  author={Torsten Ehrhardt},
  journal={Communications in Mathematical Physics},
  • T. Ehrhardt
  • Published 16 January 2004
  • Mathematics
  • Communications in Mathematical Physics
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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