Dyson's constant in the asymptotics of the Fredholm determinant of the sine kernel

2004/01/16 by Torsten Ehrhardt, Ehrhardt, Torsten · 2 citations
Mathematics · Physics and Astronomy · #47B35 #FOS: Mathematics #Functional Analysis (math.FA) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics #math.FA #msc:47B35

paper · pdf · doi:10.48550/arxiv.math/0401205

30 pages; v2: change of title, Thm.5.7 corrected, minor changes

openalex publication_date 2004/01/16 · arxiv created 2004/08/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 sin(x-y)/(x-y)/π on the interval [0,α] is given by a formula which was conjectured by F.J. Dyson. The first and second order asymptotics as well as the higher order asymptotics except for the constant term have already been proved. In this paper we thus determine the constant term.

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