190 citations · 1.9k across the 70 of their papers we have counts for
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Random Words, Toeplitz Determinants and Integrable Systems. I
Alexander R. Its, Craig A. Tracy, Harold Widom
It is proved that the limiting distribution of the length of the longest weakly increasing subsequence in an inhomogeneous random word is related to the distribution function for t…
On a Toeplitz determinant identity of Borodin and Okounkov
Estelle L. Basor, Harold Widom
The authors of the title proved an elegant identity expressing a Toeplitz determinant in terms of the Fredholm determinant of an infinite matrix which (although not described as su…
Universality of the Distribution Functions of Random Matrix Theory. II
Craig A. Tracy, Harold Widom
This paper is a brief review of recent developments in random matrix theory. Two aspects are emphasized: the underlying role of integrable systems and the occurrence of the distrib…
On the Distributions of the Lengths of the Longest Monotone Subsequences in Random Words
Craig A. Tracy, Harold Widom
We consider the distributions of the lengths of the longest weakly increasing and strongly decreasing subsequences in words of length N from an alphabet of k letters. We find Toepl…
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…