The Semicircle Law for Matrices with Independent Diagonals

被引：0

作者：

Olga Friesen

Matthias Löwe

机构：

[1] Westfälische Wilhelms-Universität Münster,Fachbereich Mathematik

来源：

Journal of Theoretical Probability | 2013年 / 26卷

关键词：

Random matrix; Semi-circle law; Dependent entries; 60K35;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real-valued entries and stochastically independent diagonals. Along the diagonals the entries may be correlated. We show that under sufficiently nice moment conditions the empirical eigenvalue distribution converges almost surely weakly to the semi-circle law.

引用

页码：1084 / 1096

页数：12

共 9 条

[1]

Arnold L.(1971)On Wigner’s semicircle law for the eigenvalues of random matrices Z. Wahrscheinlichkeitstheor. Verw. Geb. 19 191-198

[2]

Bryc W.(2006)Spectral measure of large random Hankel, Markov and Toeplitz matrices Ann. Probab. 34 1-38

[3]

Dembo A.(1994)On the eigenvalue distribution of the deformed Wigner ensemble of random matrices Adv. Sov. Math. 19 97-127

[4]

Jiang T.(2005)Semicircle law and freeness for random matrices with symmetries or correlations Math. Res. Lett. 12 531-542

[5]

Khorunzhy A.M.(1958)On the distribution of the roots of certain symmetric matrices Ann. Math. 67 325-328

[6]

Pastur L.(undefined)undefined undefined undefined undefined-undefined

[7]

Schenker J.(undefined)undefined undefined undefined undefined-undefined

[8]

Schulz-Baldes H.(undefined)undefined undefined undefined undefined-undefined

[9]

Wigner E.(undefined)undefined undefined undefined undefined-undefined

← 1 →