2022/06/13 by Sung‐Soo Byun, Byun, Sung-Soo, Christophe Charlier +1
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2206.06021
openalex publication_date 2022/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 SN of width O((1)/(N)) as N → ∞. 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 SN, as well as of several other "semi-large" gap probabilities.