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arXiv · 2401.09045

Eigenphase distributions of unimodular circular ensembles

Shinsuke Nishigaki
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Abstract

Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe recently presented a conjectured formula for the distribution of eigenphases of Haar-distributed random SU(N) matrices ($\beta$=2), supported by explicit examples at small N and by numerical samplings at larger N. In this note, I spell out a concise proof of their formula, and present its orthogonal and symplectic counterparts, i.e. the eigenphase distributions of Haar-random unimodular symmetric ($\beta$=1) and selfdual ($\beta$=4) unitary matrices parametrizing SU(N)/SO(N) and SU(2N)/Sp(2N), respectively.

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Shinsuke Nishigaki. 2024-01-17. Eigenphase distributions of unimodular circular ensembles. https://arxiv.org/abs/2401.09045

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