Open Access
Translator Disclaimer
May 2008 Borel theorems for random matrices from the classical compact symmetric spaces
Benoît Collins, Michael Stolz
Ann. Probab. 36(3): 876-895 (May 2008). DOI: 10.1214/07-AOP341


We study random vectors of the form (Tr(A(1)V), …, Tr(A(r)V)), where V is a uniformly distributed element of a matrix version of a classical compact symmetric space, and the A(ν) are deterministic parameter matrices. We show that for increasing matrix sizes these random vectors converge to a joint Gaussian limit, and compute its covariances. This generalizes previous work of Diaconis et al. for Haar distributed matrices from the classical compact groups. The proof uses integration formulas, due to Collins and Śniady, for polynomial functions on the classical compact groups.


Download Citation

Benoît Collins. Michael Stolz. "Borel theorems for random matrices from the classical compact symmetric spaces." Ann. Probab. 36 (3) 876 - 895, May 2008.


Published: May 2008
First available in Project Euclid: 9 April 2008

zbMATH: 1149.15016
MathSciNet: MR2408577
Digital Object Identifier: 10.1214/07-AOP341

Primary: 15A52 , 60F05
Secondary: 43A75 , 60B15

Keywords: central limit theorem , classical invariant theory , matrix integrals , random matrices , symmetric spaces

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 3 • May 2008
Back to Top