Determinantal structure of the overlaps for induced spherical unitary ensemble

2023/12/20 by Kohei Noda, Noda, Kohei · 1 citation
Mathematics · #33C45 #60B20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2312.12690

openalex publication_date 2023/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we study the determinantal structure of the k-th conditional expectation of the overlap for induced spherical unitary ensemble. We will show the universality for the scaling limits of the k-the conditional expectation of the overlap in the three regimes, strongly non-unitary, weakly non-unitary, and the singular origin regimes. As a consequence, we will confirm the universality for the overlap.

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• Spectral Density and Eigenvector Nonorthogonality in Complex Symmetric Random Matrices

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