139 citations · 371 across the 6 of their papers we have counts for
15 papers
The Pearcey Process
Craig A. Tracy, Harold Widom
The extended Airy kernel describes the space-time correlation functions for the Airy process, which is the limiting process for a polynuclear growth model. The Airy functions thems…
Matrix Kernels for the Gaussian Orthogonal and Symplectic Ensembles
Craig A. Tracy, Harold Widom
We derive the limiting matrix kernels for the the Gaussian Orthogonal and Symplectic ensembles scaled at the edge, with proofs of convergence in the operator norms that assure conv…
Differential Equations for Dyson Processes
Craig A. Tracy, Harold Widom
We call "Dyson process" any process on ensembles of matrices in which the entries undergo diffusion. We are interested in the distribution of the eigenvalues (or singular values) o…
A System of Differential Equations for the Airy Process
Craig A. Tracy, Harold Widom
The Airy process is characterized by its finite-dimensional distribution functions. We show that each finite-dimensional distribution function is expressible in terms of a solution…
Distribution functions for largest eigenvalues and their applications
Craig A. Tracy, Harold Widom
It is now believed that the limiting distribution function of the largest eigenvalue in the three classic random matrix models GOE, GUE and GSE describe new universal limit laws fo…
A Limit Theorem for Shifted Schur Measures
Craig A. Tracy, Harold Widom
To each partition with distinct parts we assign the probability where and are the Schur -functions and is a normalization constant. This me…