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

@article{Zhu2020TheSE,
title={The smallest eigenvalue of large Hankel matrices generated by a singularly perturbed Laguerre weight},
author={Mengkun Zhu and Yang Chen and Chuanzhong Li},
journal={arXiv: Mathematical Physics},
year={2020}
}
• Published 11 June 2020
• Mathematics
• arXiv: Mathematical Physics
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 $w_{\alpha}(x;t)$.

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