Rates of Bulk Convergence for Ensembles of Classical Compact Groups

2025/08/29 by M. Cai, Cai, Mengchun
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2508.21274

openalex publication_date 2025/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers random matrices distributed according to 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 to 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.

Citations

• Mesoscopic Rates of Convergence for Hermitian Unitary Ensembles

Cited by

• Mesoscopic Rates of Convergence for Hermitian Unitary Ensembles

Related

• Stein's method and the multivariate CLT for traces of powers on the classical compact groups
• A new approach to strong convergence II. The classical ensembles
• Rate of convergence at the hard edge for various Pólya ensembles of positive definite matrices
• A rate of convergence when generating stable invariant Hermitian random matrix ensembles
• Asymptotics for averages over classical orthogonal ensembles