戴森布朗运动和拉盖尔过程力矩过程的极限定理

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2021-03-18 DOI:10.1142/S2010326323500053

F. Nakano, Hoang Dung Trinh, Khanh Duy Trinh

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引用次数: 7

摘要

在参数β与系统大小的倒数成正比的情况下，已知高斯β系综的经验分布(p < 0.05)。\ beta拉盖尔系综)收敛于相关埃尔米特多项式的一个概率测度。拉盖尔多项式相关\)。在极限附近的高斯波动也是已知的。本文旨在研究这些结果的动态版本。更准确地说，我们研究了戴森布朗运动和拉盖尔过程，并建立了lln和clt在同一制度下的力矩过程。

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Limit theorems for moment processes of beta Dyson's Brownian motions and beta Laguerre processes

In the regime where the parameter beta is proportional to the reciprocal of the system size, it is known that the empirical distribution of Gaussian beta ensembles (resp.\ beta Laguerre ensembles) converges to a probability measure of associated Hermite polynomials (resp.\ associated Laguerre polynomials). Gaussian fluctuations around the limit have been known as well. This paper aims to study a dynamical version of those results. More precisely, we study beta Dyson's Brownian motions and beta Laguerre processes and establish LLNs and CLTs for their moment processes in the same regime.

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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.