Tracy-Widom limit for Kendall's tau

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