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 $$W_n$$ W n , the $$p_n \times q_n$$ p n × q n upper-left block of a Haar-distributed matrix, and that of $$p_nq_n$$ p n q n independent standard Gaussian random variables and show that the total variation distance converges to zero when $$p_nq_n = o(n)$$ p n q n = o ( n ) .

中文翻译：

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高斯矩阵对随机正交矩阵的全变差逼近

本文的主题是根据Haar测度分布的随机正交矩阵的条目的渐近分布。我们检查了 $$W_n$$ W n 的条目的联合分布、Haar 分布矩阵的 $$p_n \times q_n$$ pn × qn 左上块和 $$ p_nq_n$$ pnqn 独立的标准高斯随机变量，并表明当 $$p_nq_n = o(n)$$ pnqn = o ( n ) 时，总变异距离收敛为零。