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2011 Stein's Method and the Multivariate CLT for Traces of Powers on the Compact Classical Groups
Christian Döbler, Michael Stolz
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Electron. J. Probab. 16(none): 2375-2405 (2011). DOI: 10.1214/EJP.v16-960

Abstract

Let $M$ be a random element of the unitary, special orthogonal, or unitary symplectic groups, distributed according to Haar measure. By a classical result of Diaconis and Shahshahani, for large matrix size $n$, the vector of traces of consecutive powers of $M$ tends to a vector of independent (real or complex) Gaussian random variables. Recently, Jason Fulman has demonstrated that for a single power $j$ (which may grow with $n$), a speed of convergence result may be obtained via Stein's method of exchangeable pairs. In this note, we extend Fulman's result to the multivariate central limit theorem for the full vector of traces of powers.

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Christian Döbler. Michael Stolz. "Stein's Method and the Multivariate CLT for Traces of Powers on the Compact Classical Groups." Electron. J. Probab. 16 2375 - 2405, 2011. https://doi.org/10.1214/EJP.v16-960

Information

Accepted: 22 November 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1243.15023
MathSciNet: MR2861678
Digital Object Identifier: 10.1214/EJP.v16-960

Subjects:
Primary: 15B52
Secondary: 58J65, 60B15, 60F05

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