2021/11/03 by Boris A. Khoruzhenko, Khoruzhenko, Boris A., Serhii Lysychkin +1
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2111.02381
openalex publication_date 2021/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with complex eigenvalues of truncated unitary quaternion matrices equipped with the Haar measure. The joint eigenvalue probability density function is obtained for truncations of any size. We also obtain the spectral density and the eigenvalue correlation functions in various scaling limits. In the limit of strong non-unitarity the universal complex Ginibre form of the correlation functions is recovered in the spectral bulk off the real line after unfolding the spectrum. In the limit of weak non-unitarity we obtain the spectral density and eigenvalue correlation functions for all regions of interest. Off the real line the obtained expressions coincide with those previously obtained for truncations of Haar unitary complex matrices.