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

2017/06/19 by Dang-Zheng Liu, Liu, Dang-Zheng
Mathematics · #60B20 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1706.06189

openalex publication_date 2017/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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