Spherical Induced Ensembles with Symplectic Symmetry
Probability
2023-05-31 v2 Mathematical Physics
Complex Variables
math.MP
Abstract
We consider the complex eigenvalues of the induced spherical Ginibre ensemble with symplectic symmetry and establish the local universality of these point processes along the real axis. We derive scaling limits of all correlation functions at regular points both in the strong and weak non-unitary regimes as well as at the origin having spectral singularity. A key ingredient of our proof is a derivation of a differential equation satisfied by the correlation kernels of the associated Pfaffian point processes, thereby allowing us to perform asymptotic analysis.
Keywords
Cite
@article{arxiv.2209.01934,
title = {Spherical Induced Ensembles with Symplectic Symmetry},
author = {Sung-Soo Byun and Peter J. Forrester},
journal= {arXiv preprint arXiv:2209.01934},
year = {2023}
}