Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 033, 28 pages      arXiv:2209.01934      https://doi.org/10.3842/SIGMA.2023.033
Contribution to the Special Issue on Evolution Equations, Exactly Solvable Models and Random Matrices in honor of Alexander Its' 70th birthday

Spherical Induced Ensembles with Symplectic Symmetry

Sung-Soo Byun a and Peter J. Forrester b
a) Center for Mathematical Challenges, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
b) School of Mathematical and Statistics, The University of Melbourne, Victoria 3010, Australia

Received September 22, 2022, in final form May 16, 2023; Published online May 30, 2023

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.

Key words: symplectic random matrix; spherical induced ensembles; Pfaffian point process.

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