139 citations · 376 across the 11 of their papers we have counts for
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Universality of the distribution functions of random matrix theory
Craig A. Tracy, Harold Widom
This paper first surveys the connection of integrable systems of the Painleve type to various distribution functions appearing in Wigner-Dyson random matrix theory. A short discuss…
Airy Kernel and Painleve II
Craig A. Tracy, Harold Widom
We prove that the distribution function of the largest eigenvalue in the Gaussian Unitary Ensemble (GUE) in the edge scaling limit is expressible in terms of Painlevé II. Our goal…
On the Solution of a Painlevé III Equation
Harold Widom
In a 1977 paper of McCoy, Tracy and Wu there appeared for the first time the solution of a Painlevé equation in terms of Fredholm determinants of integral operators. This equation…
Asymptotics of a class of Fredholm determinants
Craig A. Tracy, Harold Widom
In this expository article we describe the asymptotics of certain Fredholm determinants which provide solutions to the cylindrical Toda equations, and we explain how these asymptot…