论文标题
领域的确定点过程的缩放限
Scaling limit for determinantal point processes on spheres
论文作者
论文摘要
具有HAAR概率度量的单一群体称为圆形单一合奏。所有特征值都位于复杂平面的单元圆上，可以将它们视为$ \ m athbb {s}^1 $的确定点过程。众所周知，随着矩阵的大小趋向于$ \ infty $，缩放点过程弱收敛到与所谓的正弦内核相关的确定点过程。我们将此结果扩展到高维球体的情况，并表明缩放限值过程是与第一类Bessel函数表达的内核相关的确定点过程。
The unitary group with the Haar probability measure is called Circular Unitary Ensemble. All the eigenvalues lie on the unit circle in the complex plane and they can be regarded as a determinantal point process on $\mathbb{S}^1$. It is also known that the scaled point processes converge weakly to the determinantal point process associated with the so-called sine kernel as the size of matrices tends to $\infty$. We extend this result to the case of high-dimensional spheres and show that the scaling limit processes are determinantal point processes associated with the kernels expressed by the Bessel functions of the first kind.
