标题： 随机正规矩阵在临界 regime 中盘计数统计的指数矩 显示英文标题

标题： Exponential moments for disk counting statistics of random normal matrices in the critical regime

摘要： 我们得到了Mittag-Leffler系综的圆盘计数统计的$m$点矩生成函数的大$n$渐近行为。 我们关注临界区域，其中所有圆盘边界以速度$n^{-\smash{\frac{1}{2}}}$合并，无论是在内部还是在边缘。 作为推论，我们得到了两个中心极限定理以及圆盘计数函数的所有联合累积量（如协方差）的精确大$n$渐近行为。 我们的结果也可以看作是具有合并平面不连续性的$n\times n$行列式的大$n$渐近行为。 显示英文摘要

摘要： 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.