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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

Abstract

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.

Citation

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Benoît Collins. Michael Stolz. "Borel theorems for random matrices from the classical compact symmetric spaces." Ann. Probab. 36 (3) 876 - 895, May 2008. https://doi.org/10.1214/07-AOP341

Information

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

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

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

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 3 • May 2008
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