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

By T. Ehrhardt. 2004

88 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/44c75144e92d20bbed4faf487a059a83e655ba96

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In Atomic and Molecular Physics, and Optics

1. Robert Buckingham
2. J. DiFranco
3. Jinho Baik

In Mathematical Physics

1. Robert Buckingham
2. J. DiFranco
3. Jinho Baik
4. Debashis Paul
5. Noureddine El Karoui
6. P. Ferrari
7. Ivan Corwin
8. S. P'ech'e

In Statistical and Nonlinear Physics

1. Robert Buckingham
2. J. DiFranco
3. Jinho Baik

Citations in the corpus

• Asymptotics of Tracy-Widom Distributions and the Total Integral of a Painlevé II Function (2007, result): “[14] Ehrhardt, T. Dyson’s constant in the asymptotics of the Fredholm determinant of the sine kernel.”