论文标题
具有一类离散旋转对称电势的确定库仑气体集合
Determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials
论文作者
论文摘要
我们考虑具有一类离散旋转对称势的确定性库仑气体集合，其液滴由几个断开的组件组成。在插入原点的点电荷下，我们得出了宏观和微观尺度中相关内核的渐近行为。在宏观尺度上，这尤其表明液滴边界上的颗粒之间存在很强的相关性。在微观范围内，这建立了边缘普遍性。对于证据，我们在矩阵里帝国 - 希尔伯特问题上使用非线性最陡的下降方法来得出相关平面正交多项式的渐近行为及其规范，直到第一个转向术语。
We consider determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials whose droplets consist of several disconnected components. Under the insertion of a point charge at the origin, we derive the asymptotic behaviour of the correlation kernels both in the macro- and microscopic scales. In the macroscopic scale, this particularly shows that there are strong correlations among the particles on the boundary of the droplets. In the microscopic scale, this establishes the edge universality. For the proofs, we use the nonlinear steepest descent method on the matrix Riemann-Hilbert problem to derive the asymptotic behaviours of the associated planar orthogonal polynomials and their norms up to the first subleading terms.
