论文标题
在几乎圆形的象征性诱导的Ginibre集合上
On the almost-circular symplectic induced Ginibre ensemble
论文作者
论文摘要
我们考虑符号诱导的吉尼伯过程，这是平面上的PFAFFIAN点过程。令$ n $为积分数。我们专注于几乎圆形的制度，其中大多数点位于薄环$ \ mathcal {s} _ {n} $ width $ o的$（\ frac {1} {n}）$ as $ n \ to \ infty $。我们的主要结果是实际轴附近所有相关函数的缩放限制，也远离真实轴。在真实轴附近，极限相关函数是具有新相关内核的PFAFFIAN，它插入了大部分同型Ginibre集合中的极限内核和抗对称的高斯高斯Hermitian Gelembles的奇数奇数。远离真实轴，极限相关函数是决定因素，而内核与出现在几乎柔米随机矩阵的大量极限中的内核相同。此外，我们获得了精确的大$ n $渐近剂，因为概率不在$ \ mathcal {s} _ {n} $之外，以及其他几个“半大差距”差距概率。
We consider the symplectic induced Ginibre process, which is a Pfaffian point process on the plane. Let $N$ be the number of points. We focus on the almost-circular regime where most of the points lie in a thin annulus $\mathcal{S}_{N}$ of width $O(\frac{1}{N})$ as $N \to \infty$. Our main results are the scaling limits of all correlation functions near the real axis, and also away from the real axis. Near the real axis, the limiting correlation functions are Pfaffians with a new correlation kernel, which interpolates the limiting kernels in the bulk of the symplectic Ginibre ensemble and of the anti-symmetric Gaussian Hermitian ensemble of odd size. Away from the real axis, the limiting correlation functions are determinants, and the kernel is the same as the one appearing in the bulk limit of almost-Hermitian random matrices. Furthermore, we obtain precise large $N$ asymptotics for the probability that no points lie outside $\mathcal{S}_{N}$, as well as of several other "semi-large" gap probabilities.
