  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.
