Another Marčenko-Pastur law for Kendall’s tau
Abstract
Bandeira et al. (2017) show that the eigenvalues of the Kendall correlation matrix of n i.i.d. random vectors in Rp are asymptotically distributed like 1∕3+(2∕3)Yq, where Yq has a Marčenko-Pastur law with parameter q=lim(p∕n) if p,n→∞ proportionately to one another. Here we show that another Marčenko-Pastur law emerges in the “ultra-high dimensional” scaling limit where p∼q′n2∕2 for some q′>0: in this quadratic scaling regime, Kendall correlation eigenvalues converge weakly almost surely to (1∕3)Yq′.
Fields of Study & Subjects
Random Matrices and Applications
Theoretical and Computational Physics
Statistical Mechanics and Entropy
Publication details
- Journal / source
- Electronic Communications in Probability
- Volume
- 31
- Issue
- none
- Publication date
- 1 January 2026