Oscillatory asymptotics for the Airy kernel determinant on two intervals

Abstract

We obtain asymptotics for the Airy kernel Fredholm determinant on two intervals. We give explicit formulas for all the terms up to and including the oscillations of order $1$, which are expressed in terms of Jacobi $\theta$-functions.

arXiv comment34 pages, 6 figures

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Cited by in corpus (2)

• The Bessel kernel determinant on large intervals and Birkhoff's ergodic theorem
• Asymptotic expansion of Toeplitz determinants of an indicator function with discrete rotational symmetry and powers of random unitary matrices