Before revision: The distributions of random matrix theory have seen an explosion of interest in recent years, and have been found in various applied fields including physics, high-dimensional statistics, wireless communications, finance, etc. The Tracy-Widom distribution is one of the most important distributions in random matrix theory, and its numerical evaluation is a subject of great practical importance.
After revision: The distributions of the k-th largest level at the soft edge scaling limit of Gaussian ensembles are some of the most important distributions in random matrix theory, and its numerical evaluation is a subject of great practical importance.