Free products of large random matrices _ a short review of recent developments

ELC International Meeting on Inference, Computation, and Spin Glasses

Burda, Zdzislaw^1

Marian Smoluchowski Institute of Physics, Mark Kac Center for Complex Systems Research, Jagiellonian University, Reymonta 4, PL30-059 Cracow, Poland^1

关键词: Eigenvalue densities;    Eigenvalue distributions;    Gaussians;    Hermitians;    Large random matrices;    Non-Hermitian matrix;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/473/1/012002/pdf
DOI  :  10.1088/1742-6596/473/1/012002

来源: IOP

【 摘 要 】

We review methods to calculate eigenvalue distributions of products of large random matrices. We discuss a generalization of the law of free multiplication to non-Hermitian matrices and give a couple of examples illustrating how to use these methods in practice. In particular we calculate eigenvalue densities of products of Gaussian Hermitian and non-Hermitian matrices including combinations of GUE and Ginibre matrices.