We consider the eigenvalues of symplectic elliptic Ginibre matrices which are known to form a Pfaffian point process whose correlation kernel can be expressed in terms of the skew-orthogonal Hermite polynomials. We derive the scaling limits and the convergence rates of the correlation functions at the real bulk/edge of the spectrum, which in particular establishes the local universality at strong non-Hermiticity. Furthermore, we obtain the subleading corrections of the edge correlation kernels, which depend on the non-Hermiticity parameter contrary to the universal leading term. Our proofs are based on the asymptotic behavior of the complex elliptic Ginibre ensemble due to Lee and Riser as well as on a version of the Christoffel–Darboux identity, a differential equation satisfied by the skew-orthogonal polynomial kernel.

我们考虑辛椭圆 Ginibre 矩阵的特征值，这些矩阵已知形成 Pfaffian 点过程，其相关核可以用斜正交 Hermite 多项式表示。我们推导了相关函数在谱的实际体积/边缘处的缩放限制和收敛率，这特别建立了强非隐性的局部普遍性。此外，我们获得了边缘相关核的次导校正，这取决于与通用导项相反的非隐性参数。我们的证明基于 Lee 和 Riser 导致的复杂椭圆 Ginibre 系综的渐近行为以及 Christoffel–Darboux 恒等式的一个版本，这是一个由斜正交多项式核满足的微分方程。