Strong Convergence of Empirical Distribution for a Class of Random Matrices

Chinese Quarterly Journal of Mathematics ›› 2006, Vol. 21 ›› Issue (1): 28-32.

Strong Convergence of Empirical Distribution for a Class of Random Matrices

Strong Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China;Key Lab of Intelligent Computing and Signal Processing of the Ministry of Education, Anhui University, Hefei 230026, China

Received:2003-10-10 Online:2006-03-30 Published:2023-12-18
About author:LlANG Qing-wen(1968-),male,native of Linzhou,Nenan,Ph.D.candidate,engages in financial engineering.
Supported by:
Supported by the NNSF of China(10471135)；

Abstract

Abstract: Let {v_ij}, i, j = 1, 2,…, be i.i.d. random variables with E_v11= 0, E²v11=1 and a_i= (a_i1,…,a_iM) be random vectors with {a_ij} being i.i.d. random variables. Define X_N=(x₁,…, X_K)and ... The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.

Key words: empirical , spectral , distribution , function, sample , covariance , matrix, Stieltjes transform, strong convergence

CLC Number:

O211.4

LIANG Qing-wen, MIAO Bai-qi, WANG Da-peng . Strong Convergence of Empirical Distribution for a Class of Random Matrices[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(1): 28-32.

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Strong Convergence of Empirical Distribution for a Class of Random Matrices

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