Random normal matrices in the almost-circular regime

IF 1.5 2区 数学 Q2 STATISTICS & PROBABILITY
Bernoulli Pub Date : 2021-12-21 DOI:10.3150/22-bej1514
Sunggyu Byun, Seong-Mi Seo
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引用次数: 13

Abstract

We study random normal matrix models whose eigenvalues tend to be distributed within a narrow"band"around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials with various boundary conditions, we derive the scaling limits of the correlation functions, some of which appear in the previous literature notably in the context of almost-Hermitian random matrices. We also obtain that fluctuations of the maximal and minimal modulus of the ensembles follow the Gumbel or exponential law depending on the boundary conditions.
概圆域中的随机正规矩阵
我们研究随机正规矩阵模型,其特征值倾向于分布在宽度与$\frac1n$成比例的单位圆周围的窄“带”内,其中$n$是矩阵的大小。对于具有各种边界条件的一般径向对称势,我们导出了相关函数的标度极限,其中一些出现在以前的文献中,特别是在几乎埃尔米特随机矩阵的情况下。我们还获得了系综的最大和最小模量的波动遵循Gumbel或指数定律,这取决于边界条件。
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来源期刊
Bernoulli
Bernoulli 数学-统计学与概率论
CiteScore
3.40
自引率
0.00%
发文量
116
审稿时长
6-12 weeks
期刊介绍: BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.
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