The smallest eigenvalue of large Hankel matrices generated by a singularly perturbed Laguerre weight

arXiv: Mathematical Physics Pub Date : 2020-06-11 DOI:10.1063/1.5140079

Mengkun Zhu, Yang Chen, Chuanzhong Li

引用次数: 2

Abstract

An asymptotic expression of the orthonormal polynomials $\mathcal{P}_{N}(z)$ as $N\rightarrow\infty$, associated with the singularly perturbed Laguerre weight $w_{\alpha}(x;t)=x^{\alpha}{\rm e}^{-x-\frac{t}{x}},~x\in[0,\infty),~\alpha>-1,~t\geq0$ is derived. Based on this, we establish the asymptotic behavior of the smallest eigenvalue, $\lambda_{N}$, of the Hankel matrix generated by the weight $w_{\alpha}(x;t)$.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

由奇异摄动拉盖尔权值生成的大汉克尔矩阵的最小特征值

导出了与奇异摄动Laguerre权$w_{\alpha}(x;t)=x^{\alpha}{\rm e}^{-x-\frac{t}{x}},~x\in[0,\infty),~\alpha>-1,~t\geq0$相关的标准正交多项式$\mathcal{P}_{N}(z)$的渐近表达式$N\rightarrow\infty$。在此基础上，我们建立了权值$w_{\alpha}(x;t)$生成的Hankel矩阵的最小特征值$\lambda_{N}$的渐近性。

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分钟内获得全文去求助

来源期刊

arXiv: Mathematical Physics

自引率

0.00%

发文量

期刊最新文献

The Non-isentropic Relativistic Euler System Written in a Symmetric Hyperbolic Form Thermodynamic formalism for generalized countable Markov shifts Chaos and Turing machines on bidimensional models at zero temperature The first order expansion of a ground state energy of the ϕ4 model with cutoffs The classical limit of mean-field quantum spin systems