Tracy.Widom limit for Kendall.s tau

In this paper, we study a high-dimensional random matrix model from nonparametric statistics called the Kendall rank correlation matrix, which is a natural multivariate extension of the Kendall rank correlation coefficient. We establish the Tracy.Widom law for its largest eigenvalue. It is the first Tracy.Widom law for a nonparametric random matrix model, and also the first Tracy.Widom law for a high-dimensional U-statistic.