Spherical induced ensembles with symplectic symmetry (Q6115279)

From authors' text: ``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.'' The paper is structured in 3 chapters: 1. Introduction and results (Proposition 1.1 (to analyse the correlation functions), Remark 1.2, Remark 1.3, Theorem 1.4 (scaling limits of the eigenvalue correlations) ); 2. Proof of Theorem 1.4 (Lemma 2.1 (structure of the correlation functions), Proposition 2.2 (large-\(N\) expansions of the differential equations), Lemma 2.3, Proof of Theorem 1.4); 3. Proof of Propositions 1.1 and 2.2 (3.1 Skew-orthogonal polynomial kernels, 3.2 Proof of Propositions 1.1, 3.3 Proof of Proposition 2.2); Appendix A; Appendix B; Acknowledgments; References (64 references).