Moderate deviations for extreme eigenvalues of beta-Laguerre ensembles

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2020-04-01 DOI:10.1142/S2010326320500033

Lei Chen, Shaochen Wang

引用次数: 0

Abstract

Let [Formula: see text] be respectively the largest and smallest eigenvalues of beta-Laguerre ensembles with parameters [Formula: see text]. For fixed [Formula: see text], under the condition that [Formula: see text] is much larger than [Formula: see text], we obtain the full moderate deviation principles for [Formula: see text] and [Formula: see text] by using the asymptotic expansion technique. Interestingly, under this regime, our results show that asymptotically the exponential tails of the extreme eigenvalues are Gaussian-type distribution tail rather than the Tracy–Widom-type distribution tail.

查看原文本刊更多论文

β - laguerre系综极端特征值的中等偏差

令[公式:见文]分别为带参数的beta-Laguerre系综的最大和最小特征值[公式:见文]。对于固定的[公式:见文]，在[公式:见文]远大于[公式:见文]的情况下，利用渐近展开技术，得到了[公式:见文]和[公式:见文]的完全中等偏差原理。有趣的是，在这种情况下，我们的结果表明，极端特征值的指数尾渐近是高斯型分布尾，而不是特雷西-威多姆型分布尾。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Random Matrices-Theory and Applications Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.90

自引率

11.10%

发文量

期刊介绍： Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics. Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory. Special issues devoted to single topic of current interest will also be considered and published in this journal.