On the almost?circular symplectic induced Ginibre ensemble

We consider the symplectic-induced Ginibre process, which is a Pfaffian point process on plane. Let N be number of points. focus almost-circular regime where most points lie in thin annulus S $\mathcal {S}_{N}$ width O 1 $O\left(\frac{1}{N}\right)$ as ? ? $N \rightarrow \infty$ . Our main results are bulk scaling limits all correlation functions near real axis, and also away from axis. Near limiting Pfaffians with new kernel, interpolates kernels symplectic ensemble antisymmetric Gaussian Hermitian odd size. Away determinants, kernel same one appearing limit almost-Hermitian random matrices. Furthermore, we obtain precise large asymptotics for probability that no outside , well several other “semi-large” gap probabilities.