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Total Variation Approximation of Random Orthogonal Matrices by Gaussian Matrices

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  • Kathryn Stewart

    (Case Western Reserve University)

Abstract

The topic of this paper is the asymptotic distribution of the entries of random orthogonal matrices distributed according to Haar measure. We examine the total variation distance between the joint distribution of the entries of $$W_n$$Wn, the $$p_n \times q_n$$pn×qn upper-left block of a Haar-distributed matrix, and that of $$p_nq_n$$pnqn independent standard Gaussian random variables and show that the total variation distance converges to zero when $$p_nq_n = o(n)$$pnqn=o(n).

Suggested Citation

  • Kathryn Stewart, 2020. "Total Variation Approximation of Random Orthogonal Matrices by Gaussian Matrices," Journal of Theoretical Probability, Springer, vol. 33(2), pages 1111-1143, June.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:2:d:10.1007_s10959-019-00900-5
    DOI: 10.1007/s10959-019-00900-5
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    References listed on IDEAS

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    1. Tiefeng Jiang & Yongcheng Qi, 2015. "Likelihood Ratio Tests for High-Dimensional Normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 988-1009, December.
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