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Strong Convergence of Empirical Distribution for a Class of Random Matrices

Strong Convergence of Empirical Distribution for a Class of Random Matrices
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摘要 Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = (ai1,…, aiM) be random vectors with {aij} being i.i.d, random variables. Define XN =(x1,…, xk) and SN =XNXN^T,where xi=ai×si and si=1/√N(v1i,…, vN,i)^T. The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.
出处 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第1期28-32,共5页 数学季刊(英文版)
基金 Supported by the NNSF of China(10471135)
关键词 empirical spectral distribution function sample covariance matrix Stieltjes transform strong convergence 协方差矩阵样本 经验光谱分布函数 Stieltjes变换 强会聚
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参考文献6

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