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

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

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