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math.PR2003★ 91 cited
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…
math.PR2003
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…