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

Dang-Zheng Liu

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arXiv · 1706.06189

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

Dang-Zheng Liu

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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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BibTeX RIS

Dang-Zheng Liu. 2017-06-19. Spectral statistics for product matrix ensembles of Hermite type with external source. https://arxiv.org/abs/1706.06189

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