Universal scaling limits of the symplectic elliptic Ginibre ensemble

Byun SS, Ebke M (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Random Matrices : Theory and Applications World Scientific

Article Number: 2250047

DOI: 10.1142/S2010326322500472

Abstract

We consider the eigenvalues of symplectic elliptic Ginibre matrices which are known to form a Pfaffian point process whose correlation kernel can be expressed in terms of the skew-orthogonal Hermite polynomials. We derive the scaling limits and the convergence rates of the correlation functions at the real bulk/edge of the spectrum, which in particular establishes the local universality at strong non-Hermiticity. Furthermore, we obtain the subleading corrections of the edge correlation kernels, which depend on the non-Hermiticity parameter contrary to the universal leading term. Our proofs are based on the asymptotic behavior of the complex elliptic Ginibre ensemble due to Lee and Riser as well as on a version of the Christoffel-Darboux identity, a differential equation satisfied by the skew-orthogonal polynomial kernel.

Authors with CRIS profile

Markus Ebke Lehrstuhl für Mathematische Stochastik

Involved external institutions

Korea Institute for Advanced Study (KIAS) / 한국 고등과학원 KR Korea, Republic of (KR)

How to cite

APA:

Byun, S.S., & Ebke, M. (2022). Universal scaling limits of the symplectic elliptic Ginibre ensemble. Random Matrices : Theory and Applications. https://dx.doi.org/10.1142/S2010326322500472

MLA:

Byun, Sung Soo, and Markus Ebke. "Universal scaling limits of the symplectic elliptic Ginibre ensemble." Random Matrices : Theory and Applications (2022).

BibTeX: Download