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

Abstract

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.

arXiv commentPreliminary Version. Comments Welcome

References in corpus (1)

• Matrix product ensembles of Hermite-type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral

Cited by in corpus (2)

• Products of Complex Rectangular and Hermitian Random Matrices
• Cyclic Pólya Ensembles on the Unitary Matrices and their Spectral Statistics