ON A GENERALIZATION OF THE ELLIPTIC LAW FOR RANDOM MATRICES

被引：6

作者：

Goetze, F. ^{[1
]}

Naumov, A. ^{[2
]}

Tikhomirov, A. ^{[3
]}

机构：

[1] Univ Bielefeld, Fac Math, Bielefeld, Germany

[2] Moscow MV Lomonosov State Univ, Fac Computat Math & Cybernet, Moscow, Russia

[3] Syktyvkar State Univ, Dept Math, Komi Res Ctr, Ural Div,RAS, Syktyvkar, Russia

来源：

ACTA PHYSICA POLONICA B | 2015年 / 46卷 / 09期

关键词：

PRODUCTS;

D O I：

10.5506/APhysPolB.46.1737

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the products of m >= 2 independent large real random matrices with independent tuples (X-jk((q)), X-kj((q))), 1 <= j < k <= n of entries. The entries X-jk((q)), X-kj((q)) are standardized and correlated with correlation coefficient rho = E[X-jk((q)) X-kj((q))]. The limit distribution of the empirical spectral distribution of the eigenvalues of such products does not depend on rho and is equal to the distribution of the mth power of a uniformly distributed random variable on the unit disc.

引用

页码：1737 / 1745

页数：9

共 14 条

[1] Around the circular law
Bordenave, Charles
Chafai, Djalil
[J]. PROBABILITY SURVEYS, 2012, 9 : 1 - 89
[2] Girko V. L., 1985, TEOR VEROYATNOST PRI, V30, P640
[3] Gotze F., ARXIV14047013MATHPR
[4] Gotze F., ARXIV13095711MATHPR
[5] Gotze F., ARXIVMATH0702386MATH
[6] Gotze F., ARXIV10122710MATHPR
[7] THE CIRCULAR LAW FOR RANDOM MATRICES
Gotze, Friedrich
Tikhomirov, Alexander
[J]. ANNALS OF PROBABILITY, 2010, 38 (04) : 1444 - 1491
[8] Naumov A., ARXIV12011639MATHPR
[9] Naumov A.A., 2013, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., P31
[10] Nguyen H., 2014, THE ELLIPTIC LAW

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