Determinants of Airy Operators and Applications to Random Matrices

Abstract

The purpose of this paper is to describe asymptotic formulas for determinants of certain operators that are analogues of Wiener-Hopf operators. The determinant formulas yield information about the distribution functions for certain random variables that arise in random matrix theory when one rescales at the edge of the spectrum.

LaTeX file. 17 pages. An error corrected

References in corpus (2)

• Finite N Fluctuation Formulas for Random Matrices
• Distribution Functions for Random Variables for Ensembles of positive Hermitian Matrices

Cited by in corpus (13)

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• Linear statistics and pushed Coulomb gas at the edge of beta random matrices: four paths to large deviations
• Large gap asymptotics for Airy kernel determinants with discontinuities
• Gaussian fluctuation for the number of particles in Airy, Bessel, sine and other determinantal random point fields
• Fredholm determinant solutions of the Painlevé II hierarchy and gap probabilities of determinantal point processes
• Linear Statistics of Random Matrix Ensembles at the Spectrum Edge Associated with the Airy Kernel
• Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices
• On fluctuations of global and mesoscopic linear eigenvalue statistics of generalized Wigner matrices
• A fully noncommutative Painlevé II hierarchy: Lax pair and solutions related to Fredholm determinants
• Phase transitions and random matrices
• Deviations from the Circular Law
• Unitary transform diagonalizing the Confluent Hypergeometric kernel
• Gaussian limit for determinantal point processes with $J$-Hermitian kernels