Oscillatory Asymptotics for the Airy Kernel Determinant on Two Intervals

2019/12/31 by Elliot Blackstone, Christophe Charlier, Jonatan Lenells · 10 citations
Mathematics · Physics and Astronomy · #Airy function #Fredholm determinant #Fredholm integral equation #Fredholm theory #Kernel (algebra) #Mathematical functions and polynomials #Order (exchange) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math-ph #math.MP

paper · pdf · doi:10.1093/imrn/rnaa205

published in International Mathematics Research Notices 2022(4), 2636-2687 (Oxford University Press) · 34 pages, 6 figures

openalex publication_date 2020/07/24 · arxiv created 2020/09/04 · arxiv updated 2020/09/07 · openalex created_date 2020/09/11 · openalex updated_date 2026/08/05

Abstract

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 θ -functions.

Citations

• A Steepest Descent Method for Oscillatory Riemann--Hilbert Problems. Asymptotics for the MKdV Equation
• DIFFERENTIAL EQUATIONS FOR QUANTUM CORRELATION FUNCTIONS
• Universality at the edge of the spectrum for unitary, orthogonal, and symplectic ensembles of random matrices
• Determinantal random point fields
• On the numerical evaluation of Fredholm determinants