论文标题
雅各比统一合奏的最小特征值分布
The Smallest Eigenvalue Distribution of the Jacobi Unitary Ensembles
论文作者
论文摘要
在重量$ x^α（1-x）^β，〜x \ [0,1]，〜α，β> 0 $中产生的jacobi单位合奏的硬边缩放限制中，该hermitian矩阵的所有特征均在此间隔$ [t，1] $中给出了BESS的概率。我们得出了该贝塞尔 - 内核决定因素的渐近学中的常数。结果的专业化给出了间隔$（ - a，a），a> 0，$没有雅各比单位合奏中的特征值$（1-x x^2）^β，x \ in [-1,1,1] $的差异不存在。
In the hard edge scaling limit of the Jacobi unitary ensemble generated by the weight $x^α(1-x)^β,~x\in[0,1],~α,β>0$, the probability that all eigenvalues of Hermitian matrices from this ensemble lie in the interval $[t,1]$ is given by the Fredholm determinant of the Bessel kernel. We derive the constant in the asymptotics of this Bessel-kernel determinant. A specialization of the results gives the constant in the asymptotics of the probability that the interval $(-a,a),a>0,$ is free of eigenvalues in the Jacobi unitary ensemble with the symmetric weight $(1-x^2)^β, x\in[-1,1]$.
