Dyson's constants in the asymptotics of the determinants of Wiener-Hopf-Hankel operators with the sine kernel
Abstract
In this paper we are going to prove two asymptotic formulas for determinants det(I-Ks), as s goes to infinity, where Ks are the Wiener-Hopf-Hankel operators acting on L2[0,s] with the kernels K(x-y)+K(x+y) and K(x-y)-K(x+y), respectively, and K(t):=sin(t)/(π*t). These formulas were conjectured by Dyson. The identification of the constant term in the asymptotics was an open problem for a long time.
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