论文标题
硬墙附近二维库仑气体的边缘行为
Edge behavior of two-dimensional Coulomb gases near a hard wall
论文作者
论文摘要
当外部电势对称时，我们考虑限制在磁盘上的二维库仑气体。在有效改变平衡的硬壁约束的情况下，平衡度量的密度在硬壁上获得了一个单数组件。在决定性情况下，我们研究了硬壁上库仑颗粒的局部统计数据，并证明其局部相关性是用“拉普拉斯型”积分来表达的，这些积分出现在弱非产权方面的截断单位矩阵的背景下。
We consider a two-dimensional Coulomb gas confined to a disk when the external potential is radially symmetric. In the presence of a hard-wall constraint effective to change the equilibrium, the density of the equilibrium measure acquires a singular component at the hard wall. In the determinantal case, we study the local statistics of Coulomb particles at the hard wall and prove that their local correlations are expressed in terms of "Laplace-type" integrals, which appear in the context of truncated unitary matrices in the regime of weak non-unitarity.
