Spectral statistics for product matrix ensembles of Hermite type with external source

Dang-Zheng Liu

Published 2017-06-19Version 1

We continue investigating spectral properties of a Hermitised random matrix product, which, contrary to previous product ensembles, allows for eigenvalues on the full real line. When a GUE matrix with an external source is involved, we prove that the eigenvalues of the product form a determinantal point process and derive a double integral representation for correlation kernel. As the source changes, we observe a critical value and establish the existence of a phase transition for scaled eigenvalues at the origin. Particularly in the critical case, we obtain a new family of Pearcey-type kernels.