Rates of bulk convergence for ensembles of classical compact groups
Abstract
This paper considers random matrices distributed according to the Haar measure in different classical compact groups. Utilizing the determinantal point structures of their nontrivial eigenangles, with respect to the L1-Wasserstein distance, we obtain the rate of convergence for different ensembles towards the sine point process when the dimension of matrices N is sufficiently large. Specifically, the rate is roughly of order N−2 on the unitary group and of order N−1 on the orthogonal group and the compact symplectic group.
Fields of Study & Subjects
Random Matrices and Applications
Stochastic processes and statistical mechanics
Advanced Operator Algebra Research
Publication details
- Journal / source
- Electronic Communications in Probability
- Volume
- 31
- Issue
- none
- Pages
- 1–9
- Publication date
- 1 January 2026
- Language
- EN