[HG_AP] Three topological phases of the elliptic Ginibre ensembles with a point charge
ABSTRACT
In the large $N$ limit, complex and symplectic random matrix models exhibit limiting spectra whose support is called the droplets. In this talk, we will discuss the elliptic Ginibre ensemble conditioned to have real eigenvalue with multiplicity proportional to the dimension of the matrix. We prove that the droplets are either simply connected, doubly connected, or composed of two simply connected components. Moreover, we present the explicit description of the droplet and electrostatic energies for the simply and doubly connected case. Finally, we introduce the asymptotic behavior of the moments of the characteristic polynomials of elliptic Ginibre matrices as an application. This is a joint work with Sung-Soo Byun.
arXiv:2502.02948