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  • 學位論文

廣義隨機矩陣特徵值之中央極限定理

Central Limit Theorem for Linear Eigenvalue Statistics of Generalized Wigner Matrices

指導教授 : 張志中
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摘要


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並列摘要


In this paper, we consider n×n real symmetric Wigner matrices W with independent (modulo symmetry condition), but not necessarily identically distributed, entries {W_jk }_(j,k=1)^n and prove central limit theorem for linear eigenvalue statistics of such matrices.

參考文獻


[1] A. Lytova and L.Pastur.(2009). Central limit theorem for linear eigenvalue statistics of random
[2] La ́szlo ́ Erdo ̈s,Horng-Tzer Yau,and Jun Yin.(2010). Rigidity of eigenvalues of generalized
Wigner matrices. Advances in Mathematics, Volume 229, Issue 3, 15 February 2012, Pages
[3] Arharov, L. V.(1971). Limit theorems for the characteristic roots of a sample covariance
matrix.Dokl. Akad. Nauk. SSSR 199 994-997.

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