论文标题
由奇异的laguerre重量产生的大汉克尔矩阵的最小特征值
The smallest eigenvalue of large Hankel matrices generated by a singularly perturbed Laguerre weight
论文作者
论文摘要
正顺式多项式的渐近表达$ \ Mathcal {p} _ {n}（z）$作为$ n \ rightarrow \ rightarrow \ infty $，与奇异扰动的laguerre wegert $w_α（x; t）= x^α{\ rm相关e}^{ - x- \ frac {t} {x}}，〜x \ in [0，\ infty），〜α> -1，〜t \ geq0 $已得出。基于此，我们建立了由权重$w_α（x; t）$生成的hankel矩阵的最小特征值的渐近行为，即$λ_{n} $。
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 $w_α(x;t)$.
