Central limit theorems for multivariate Bessel processes in the freezing regime II: The covariance matrices
Central limit theorems for multivariate Bessel processes in the freezing regime II: The covariance matrices
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冻结状态下多元贝塞尔过程的中心极限定理 II：协方差矩阵
DOI：
10.1016/j.jat.2019.07.002
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发表时间：
2019
影响因子：
0.9
通讯作者：
Voit Michael
中科院分区：
文献类型：
--
作者：
Andraus Sergio;Voit Michael
N维Bessel过程(Xt，k)t≥0通过相关的根系和重数常数k≥0进行分类.它们描述了与N个粒子相互作用的Calogero-Moser-Sutherland粒子系统，并与β-Hermite和β-Laguerre系综有关。最近，关于固定t>；0，固定起点和k→∞，得到了几个中心极限定理。本文利用相应Bessel函数的一个极限结果，将A-情形下的CLT从0中开始推广到任意开始分布。我们还确定了高斯极限协方差矩阵的本征值和本征向量，并研究了它在k→∞和N→∞的中间粒子共振子理论中的应用。
Bessel processes (X t, k) t≥ 0 in N dimensions are classified via associated root systems and multiplicity constants k≥ 0. They describe interacting Calogero–Moser–Sutherland particle systems with N particles and are related to β-Hermite and β-Laguerre ensembles. Recently, several central limit theorems were derived for fixed t> 0, fixed starting points, and k→∞. In this paper we extend the CLT in the A-case from start in 0 to arbitrary starting distributions by using a limit result for the corresponding Bessel functions. We also determine the eigenvalues and eigenvectors of the covariance matrices of the Gaussian limits and study applications to CLTs for the intermediate particles for k→∞ and then N→∞.