FLUCTUATIONS OF EIGENVALUES OF RANDOM NORMAL MATRICES

被引：101
作者：
Ameur, Yacin [1 ]
Hedenmalm, Hakan [2 ]
Makarov, Nikolai [3 ]
机构：
[1] Lulea Univ Technol, Dept Math, S-97187 Lulea, Sweden
[2] Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden
[3] CALTECH, Dept Math, Pasadena, CA 91125 USA
来源：
DUKE MATHEMATICAL JOURNAL | 2011年 / 159卷 / 01期
基金：
美国国家科学基金会;
关键词：
LIMIT; ZEROS; FUNCTIONALS;
D O I：
10.1215/00127094-1384782
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, we consider a fairly general potential in the plane and the corresponding Boltzmann-Gibbs distribution of eigenvalues of random normal matrices. As the order of the matrices tends to infinity, the eigenvalues condensate on a certain compact subset of the plane-the "droplet." We prove that fluctuations of linear statistics of eigenvalues of random normal matrices converge on compact subsets of the interior of the droplet to a Gaussian field, and we discuss various ramifications of this result.
引用
收藏
页码：31 / 81
页数：51
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