Total Variation Approximation of Random Orthogonal Matrices by Gaussian Matrices

Kathryn Stewart ()
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Kathryn Stewart: Case Western Reserve University

Journal of Theoretical Probability, 2020, vol. 33, issue 2, 1111-1143

Abstract: 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).

Keywords: Random orthogonal matrix; Central limit theorem; Wishart matrices; Moments; 60F05; 60C05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00900-5

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