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-K_s), as s goes to infinity, where K_s are the Wiener-Hopf-Hankel operators acting on L^2[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.

proof of Thm. 3.2 corrected; introduction extended

References in corpus (2)

• On the asymptotics of certain Wiener-Hopf-plus-Hankel determinants
• Gap probability in the spectrum of random matrices and asymptotics of polynomials orthogonal on an arc of the unit circle

Cited by in corpus (4)

• Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function
• Total integrals of global solutions to Painleve II
• Weak and strong confinement in the Freud random matrix ensemble and gap probabilities
• Entanglement entropies of an interval in the free Schrödinger field theory on the half line