标题： 弗洛伊德酉系综最小特征值分布的渐进行为 显示英文标题

标题： Asymptotics of the Smallest Eigenvalue Distributions of Freud Unitary Ensembles

摘要： 我们考虑一些弗洛德酉系综的最小特征值分布，即来自这些系综的厄米特矩阵的所有特征值位于区间$(t,\infty)$的概率。 这个问题与由具有跳跃间断点的弗洛德权函数生成的汉克尔行列式有关。 通过使用陈和伊萨姆的阶梯算子方法，我们得到了相应正交多项式的递推系数的离散系统。 这使我们能够通过迪森的库仑流体方法推导出递推系数的大型$n$渐近行为。 最后，我们通过递推系数之间的关系以及借助文献中的一些最新结果，得到了汉克尔行列式的大型$n$渐近行为以及这些概率的渐近行为。 显示英文摘要

摘要： We consider the smallest eigenvalue distributions of some Freud unitary ensembles, that is, the probabilities that all the eigenvalues of the Hermitian matrices from the ensembles lie in the interval $(t,\infty)$. This problem is related to the Hankel determinants generated by the Freud weights with a jump discontinuity. By using Chen and Ismail's ladder operator approach, we obtain the discrete systems for the recurrence coefficients of the corresponding orthogonal polynomials. This enables us to derive the large $n$ asymptotics of the recurrence coefficients via Dyson's Coulomb fluid approach. We finally obtain the large $n$ asymptotics of the Hankel determinants and that of the probabilities from their relations to the recurrence coefficients and with the aid of some recent results in the literature.