论文标题
磁盘计数的指数矩计算临界状态中随机正常矩阵的统计量
Exponential moments for disk counting statistics of random normal matrices in the critical regime
论文作者
论文摘要
我们获得了$ M $ $ $ n $渐变的大型渐近级 - 点矩生成的磁盘计数统计数据的函数。我们专注于关键制度，其中所有磁盘边界都以速度$ n^{ - \ smash {\ frac {\ frac {1} {2}}} $合并，无论是在散装还是边缘。作为推论，我们获得了两个中心限制定理，并获得了所有联合累积物（例如磁盘计数函数的协方差）的精确$ n $渐近学。我们的结果也可以看作是与$ n \ times n $决定因素与平面不连续性的大型$ n $渐近技术。
We obtain large $n$ asymptotics for the $m$-point moment generating function of the disk counting statistics of the Mittag-Leffler ensemble. We focus on the critical regime where all disk boundaries are merging at speed $n^{-\smash{\frac{1}{2}}}$, either in the bulk or at the edge. As corollaries, we obtain two central limit theorems and precise large $n$ asymptotics of all joint cumulants (such as the covariance) of the disk counting function. Our results can also be seen as large $n$ asymptotics for $n\times n$ determinants with merging planar discontinuities.
